Thursday, April 20, 2017

The Relationships Between Elves and Dwarves Throughout the Ages

*This essay follows my Tolkien Canon Policy. Anything that does not contradict the text(s) above it is considered canon. Lord of the Rings is the first tier; The Hobbit, The Silmarillion, and The Children of Húrin are the second tier (as all – in some way – were not fully complete like LotR; however they are all individual books in their own right); and all other works and notes are in the third tier.

It may stand out to you that I do not use any quotes from The Hobbit in this essay. That is because this essay is about the bigger Middle-earth mythology, and The Hobbit was not written with the intention of being part of the bigger mythology, thus leading to numerous inconsistencies that cannot be reconciled. *

Many people seem to be confused about the depth of Gimli's feelings for Galadriel, especially in comparison to his friendship with Legolas. I have also seen much confusion on the matter of elf/dwarf history overall. It is a complicated matter that depends not only on what time in Middle-earth's history you are speaking of, but also on what clan of elf or dwarf you are speaking of.

Therefore, I have covered all elven and dwarven interaction throughout all of Middle-earth's history in this essay.

Bold in the quotes is my emphasis.
But Ilúvatar spoke again and said: “Even as I gave being to the thoughts of the Ainur at the beginning of the World, so now I have taken up thy desire and given to it a place therein; but in no other way will I amend thy handiwork, and as thou hast made it, so shall it be. But I will not suffer this: that these should come before the Firstborn of my design, nor that thy impatience should be rewarded. They shall sleep now in the darkness under stone, and shall not come forth until the Firstborn have awakened upon Earth; and until that time thou and they shall wait, though long it seem. But when the time comes I will awaken them, and they shall be to thee as children; and often strife shall arise between thine and mine, the children of my adoption and the children of my choice.” - The Silmarillion, Of Aulë and Yavanna
This quote seems to be the basis for most peoples belief that any positive elf/dwarf relation is 'unnatural' or 'other'.

Middle-earth's history shows otherwise. We see several close bonds between elves and dwarves, throughout all three ages. We also have conflicts, throughout all three ages. I'm going in chronological order; otherwise this would be a nightmare of an explanation!
They say also that the Seven Fathers of the Dwarves return to live again in their own kin and to bear once more their ancient names: of whom Durin was the most renowned in after ages, father of that kindred most friendly to the Elves, whose mansions were at Khazad-dûm. - The Silmarillion, Of Aulë and Yavanna
This is contradicted by the text, since we will see the dwarves of Nogrod and Belegost have close relationships with elves.
For Mîm came of Dwarves that were banished in ancient days from the great Dwarf-cities of the east, and long before the return of Morgoth they wandered westward into Beleriand; but they became diminished in stature and in smith-craft, and they took to lives of stealth, walking with bowed shoulders and furtive steps. Before the Dwarves of Nogrod and Belegost came west over the mountains the Elves of Beleriand knew not what these others were, and they hunted them, and slew them; but afterwards they let them alone, and they were called Noegyth Nibin, the Petty-Dwarves, in the Sindarin tongue. They loved none but themselves, and if they feared and hated the Orcs, they hated the Eldar no less, and the Exiles most of all; for the Noldor, they said, had stolen their lands and their homes. - The Silmarillion, Of Túrin Turambar
Quendi and Eldar goes into more detail about this:
The Eldar did not at first recognize these as Incarnates, for they seldom caught sight of them in clear light. They only became aware of their existence indeed when they attacked the Eldar by stealth at night, or if they caught them alone in wild places. The Eldar therefore thought that they were a kind of cunning two-legged animals living in caves, and they called them Levain tad-dail [1], or simply Tad-dail, and they hunted them. But after the Eldar had made the acquaintance of the Naugrim, the Tad-dail were recognized as a variety of Dwarves and were left alone. There were then few of them surviving, and they were very wary, and too fearful to attack any Elf, unless their hiding-places were approached too nearly. The Sindar gave them the names Nogotheg 'Dwarf-let', or Nogoth niben 'Petty Dwarf'. 
The great Dwarves despised the Petty-dwarves, who were (it is said) the descendants of Dwarves who had left or been driven out from the Communities, being deformed or undersized, or slothful and rebellious. But they still acknowledged their kinship and resented any injuries done to them. Indeed it was one of their grievances against the Eldar that they had hunted and slain their lesser kin, who had settled in Beleriand before the Elves came there. This grievance was set aside, when treaties were made between the Dwarves and the Sindar, in consideration of the plea that the Petty-dwarves had never declared themselves to the Eldar, nor presented any claims to land or habitations, but had at once attacked the newcomers in darkness and ambush. But the grievance still smouldered, as was later seen in the case of Mim, the only Petty-dwarf who played a memorable part in the Annals of Beleriand. The Noldor, for use in Quenya, translated these Sindarin names for the Petty-dwarves by Attalyar 'Bipeds', and Pikinau-kor or Pitya-naukor- The War of the Jewels, Quendi and Eldar
The Sindar were attacked by the petty-dwarves, and were not given the chance to figure out what they were. The dwarves still took offense at first, but later agreed with and accepted the elves explanation, and officially forgave them.
Themselves they named Khazâd, but the Sindar called them Naugrim, the Stunted People, and Gonnhirrim, Masters of Stone. Far to the east were the most ancient dwellings of the Naugrim, but they had delved for themselves great halls and mansions, after the manner of their kind, in the eastern side of Ered Luin; and those cities were named in their own tongue Gabilgathol and Tumunzahar. To the north of the great height of Mount Dolmed was Gabilgathol, which the Elves interpreted in their tongue Belegost, that is Mickleburg; and southward was delved Tumunzahar, by the Elves named Nogrod, the Hollowbold. Greatest of all the mansions of the Dwarves was Khazâd-dûm, the Dwarrowdelf, Hadhodrond in the Elvish tongue, that was afterwards in the days of its darkness called Moria; but it was far off in the Mountains of Mist beyond the wide leagues of Eriador, and to the Eldar came but as a name and a rumour from the words of the Dwarves of the Blue Mountains. 
From Nogrod and Belegost the Naugrim came forth into Beleriand; and the Elves were filled with amazement, for they had believed themselves to be the only living things in Middle-earth that spoke with words or wrought with hands, and that all others were but birds and beasts. But they could understand no word of the tongue of the Naugrim, which to their ears was cumbrous and unlovely; and few ever of the Eldar have achieved the mastery of it. But the Dwarves were swift to learn, and indeed were more willing to learn the Elventongue than to teach their own to those of alien race. Few of the Eldar went ever to Nogrod and Belegost, save Eöl of Nan Elmoth and Maeglin his son; but the Dwarves trafficked into Beleriand, and they made a great road that passed under the shoulders of Mount Dolmed and followed the course of the River Ascar, crossing Gelion at Sarn Athrad, the Ford of Stones, where battle after befell. Ever cool was the friendship between the Naugrim and the Eldar, though much profit they had one of the other; but at that time those griefs that lay between them had not yet come to pass, and King Thingol welcomed them. But the Naugrim gave their friendship more readily to the Noldor in after days than to any others of Elves and Men, because of their love and reverence for Aulë; and the gems of the Noldor they praised above all other wealth. In the darkness of Arda already the Dwarves wrought great works, for even from the first days of their Fathers they had marvellous skill with metals and with stone; but in that ancient time iron and copper they loved to work, rather than silver or gold. - The Silmarillion, Of the Sindar
From the very beginning the elves insulted the dwarves by calling them 'stunted'. We know that this will become the main Sindarin word for dwarves. We learn many Khuzdul place names here, which will continue in LotR. However, few elves mastered Khuzdul; mainly because they didn't like how it sounded.

This part tells us that Thingol and the Sindar were not close friends with the dwarves, but that the issues between the Sindar and the dwarves had yet to happen. This will become very important in the following Ages. The text goes on to state that the Noldor got along much better with the dwarves than the Sindar did. That is also a very important distinction.

Quendi and Eldar also covers this:
The Sindar had long known the Dwarves, and had entered into peaceful relations with them, though of trade and exchange of skills rather than of true friendship, before the coming of the Exiles. The name (in the plural) that the Dwarves gave to themselves was Khazad, and this the Sindar rendered as they might in the terms of their own speech, giving it the form *chadod > *chadaud > Hadhod. (Note 22, p. 412) Hadhod, Hadhodrim was the name which they continued to use in actual intercourse with the Dwarves; but among themselves they referred to the Dwarves usually as the Naugrim 'the Stunted Folk'. The adjective naug 'dwarf(ed), stunted', however, was not used by itself for one of the Khazad. The word used was Nogoth, pl. Noegyth, class-plural Nogothrim (as an occasional equivalent of Naugrim). (Note 23, p. 413) They also often referred to the Dwarves as a race by the name Dornhoth 'the Thrawn Folk', because of their stubborn mood as well as bodily toughness. 
The Exiles heard of the Dwarves first from the Sindar, and when using the Sindarin tongue naturally adopted the already established names. But later in Eastern Beleriand the Noldor came into independent relations with the Dwarves of Eryd Lindon, and they adapted the name Khazad anew for use in Quenya, giving it the form Kasar, pl. Kasari or Kasari. (Note 24, p. 413) This was the word most commonly used in Quenya for the Dwarves, the partitive plural being Kasalli, and the race-name Kasallie. But the Sindarin names were also adapted or imitated, a Dwarf being called Nauko or Norno (the whole people Naukalie or Nornalie). Norno was the more friendly term. (Note 25, p. 413) 
Note 7 (p. 377). 
The Dwarves were in a special position. They claimed to have known Beleriand before even the Eldar first came there; and there do appear to have been small groups dwelling furtively in the highlands west of Sirion from a very early date: they attacked and waylaid the Elves by stealth, and the Elves did not at first recognize them as Incarnates, but thought them to be some kind of cunning animal, and hunted them. By their own account they were fugitives, driven into the wilderness by their own kin further east, and later they were called the Noegyth Nibin (32) or Petty-dwarves, for they had become smaller than the norm of their kind, and filled with hate for all other creatures. 
When the Elves met the powerful Dwarves of Nogrod and Belegost, in the eastern side of the Mountains, they recognized them as Incarnates, for they had skill in many crafts, and learned the Elvish speech readily for purposes of traffic. At first the Elves were in doubt concerning them, believing them to be related to Orcs and creatures of Morgoth; but when they found that, though proud and unfriendly, they could be trusted to keep any treaties that they made, and did not molest those who left them in peace, they traded with them and let them come and go as they would. They no longer classed them as Moerbin, but neither did they ever reckon them as Celbin, calling them the Dornhoth ('the thrawn folk') or the Naugrim ('the stunted people'). [See further on the Petty-dwarves pp. 388 – 9.] - The War of the Jewels, Quendi and Eldar
Since The Silmarillion takes precedence, we know that Naugrim and Gonnhirrim were the two main names used by the Sindar. However, that does not mean these other names were not used – they just did not become the two main ones. This is also the only source we have for the Noldorin names.

The first meetings between the dwarves and Sindar were tense (for good reason), but they seem to have quickly come to acknowledge one another and forge a business relationship.
Now Melian had much foresight, after the manner of the Maiar; and when the second age of the captivity of Melkor had passed, she counseled Thingol that the Peace of Arda would not last for ever. He took thought therefore how he should make for himself a kingly dwelling, and a place that should be strong, if evil were to awake again in Middle-earth; and he sought aid and counsel of the Dwarves of Belegost. They gave it willingly, for they were unwearied in those days and eager for new works; and though the Dwarves ever demanded a price for all that they did, whether with delight or with toil, at this time they held themselves paid. For Melian taught them much that they were eager to learn, and Thingol rewarded them with many fair pearls. These Círdan gave to him, for they were got in great number in the shallow waters about the Isle of Balar; but the Naugrim had not before seen their like, and they held them dear. One there was as great as a dove's egg, and its sheen was as starlight on the foam of the sea; Nimphelos it was named, and the chieftain of the Dwarves of Belegost prized it above a mountain of wealth. - The Silmarillion, Of the Sindar
Though they were not close friends, the Sindar and the dwarves trusted each other. They sought and gave aid willingly. They had large amounts of trade, and were good business partners (good quality pearls and Melian's knowledge are not insignificant gifts).
Therefore the Naugrim laboured long and gladly for Thingol, and devised for him mansions after the fashion of their people, delved deep in the earth. Where the Esgalduin flowed down, and parted Neldoreth from Region, there rose in the midst of the forest a rocky hill, and the river ran at its feet. There they made the gates of the hall of Thingol, and they built a bridge of stone over the river, by which alone the gates could be entered. Beyond the gates wide passages ran down to high halls and chambers far below that were hewn in the living stone, so many and so great that that dwelling was named Menegroth, the Thousand Caves. - The Silmarillion, Of the Sindar
The dwarves were not only happy to help the Sindar, but also share with them some of their culture.
But the Elves also had part in that labour, and Elves and Dwarves together, each with their own skill, there wrought out the visions of Melian, images of the wonder and beauty of Valinor beyond the Sea. The pillars of Menegroth were hewn in the likeness of the beeches of Oromë, stock, bough, and leaf, and they were lit with lanterns of gold. The nightingales sang there as in the gardens of Lórien; and there were fountains of silver, and basins of marble, and floors of many-coloured stones. Carven figures of beasts and birds there ran upon the walls, or climbed upon the pillars, or peered among the branches entwined with many flowers. And as the years passed Melian and her maidens filled the halls with woven hangings wherein could be read the deeds of the Valar, and many things that had befallen in Arda since its beginning, and shadows of things that were yet to be. That was the fairest dwelling of any king that has ever been east of the Sea. - The Silmarillion, Of the Sindar
Together, elves and dwarves can create unparalleled works of beauty. You will see, something amazing always happens when elves and dwarves work together.
And when the building of Menegroth was achieved, and there was peace in the realm of Thingol and Melian, the Naugrim yet came ever and anon over the mountains and went in traffic about the lands; but they went seldom to the Falas, for they hated the sound of the sea and feared to look upon it. To Beleriand there came no other rumour or tidings of the world without. - The Silmarillion, Of the Sindar
The dwarves had an open invitation to Doriath, and they travelled throughout the realm; continuing to spend much of their time with the elves.
But as the third age of the captivity of Melkor drew on, the Dwarves became troubled, and they spoke to King Thingol, saying that the Valar had not rooted out utterly the evils of the North, and now the remnant, having long multiplied in the dark, were coming forth once more and roaming far and wide. “There are fell beasts,” they said, “in the land east of the mountains, and your ancient kindred that dwell there are flying from the plains to the hills.” - The Silmarillion, Of the Sindar
The dwarves trusted Thingol with their worries, and warned him about the growing darkness.
And ere long the evil creatures came even to Beleriand, over passes in the mountains, or up from the south through the dark forests. Wolves there were, or creatures that walked in wolf- shapes, and other fell beings of shadow; and among them were the Orcs, who afterwards wrought ruin in Beleriand: but they were yet few and wary, and did but smell out the ways of the land, awaiting the return of their lord. Whence they came, or what they were, the Elves knew not then, thinking them perhaps to be Avari who had become evil and savage in the wild; in which they guessed all too near, it is said. 
Therefore Thingol took thought for arms, which before his people had not needed, and these at first the Naugrim smithied for him; for they were greatly skilled in such work, though none among them surpassed the craftsmen of Nogrod, of whom Telchar the smith was greatest in renown. A warlike race of old were all the Naugrim, and they would fight fiercely against whomsoever aggrieved them: servants of Melkor, or Eldar, or Avari, or wild beasts, or not seldom their own kin, Dwarves of other mansions and lordships. Their smithcraft indeed the Sindar soon learned of them; yet in the tempering of steel alone of all crafts the Dwarves were never outmatched even by the Noldor, and in the making of mail of linked rings, which was first contrived by the smiths of Belegost, their work had no rival. - The Silmarillion, Of the Sindar
The dwarves not only made weapons with the Sindar, but also taught them their smithcraft – once again sharing a fundamental part of their culture. It is stated that not even the Noldor could outdo dwarves in this, so the Sindar's work would not be as good quality as the dwarves'.
At this time therefore the Sindar were well-armed, and they drove off all creatures of evil, and had peace again; but Thingol's armouries were stored with axes and with spears and swords, and tall helms, and long coats of bright mail; for the hauberks of the Dwarves were so fashioned that they rusted not but shone ever as if they were new-burnished. And that proved well for Thingol in the time that was to come. - The Silmarillion, Of the Sindar
The Sindar were only allowed to triumph because of the dwarves' help.
The Cirth were devised first in Beleriand by the Sindar, and were long used only for inscribing names and brief memorials upon wood or stone. [cut] The Cirth in their older and simpler form spread eastward in the Second Age, and became known to many peoples, to Men and Dwarves, and even to Orcs, all of whom altered them to suit their purposes and according to their skill or lack of it. One such simple form was still used by the Men of Dale, and a similar one by the Rohirrim. 
But in Beleriand, before the end of the First Age, the Cirth, partly under the influence of the Tengwar of the Noldor, were rearranged and further developed. Their richest and most ordered form was known as the Alphabet of Daeron, the minstrel and loremaster of King Thingol of Doriath. Among the Eldar the Alphabet of Daeron did not develop true cursive forms, since for writing the Elves adopted the Fëanorian letters. The Elves of the West indeed for the most part gave up the use of runes altogether. In the country of Eregion, however, the Alphabet of Daeron was maintained in use and passed thence to Moria, where it became the alphabet most favoured by the Dwarves. It remained ever in use among them and passed with them to the North. [cut] As with their speech the Dwarves made use of such scripts as were current and many wrote the Fëanorian letters skillfully; but for their own tongue they adhered to the Cirth, and developed written pen-forms from them. - Lord of the Rings, Appendix E 
In those days, it is said, Daeron the Minstrel, chief loremaster of the kingdom of Thingol, devised his Runes; and the Naugrim that came to Thingol learned them, and were well- pleased with the device, esteeming Daeron's skill higher than did the Sindar, his own people. By the Naugrim the Cirth were taken east over the mountains and passed into the knowledge of many peoples; but they were little used by the Sindar for the keeping of records, until the days of the War, and much that was held in memory perished in the ruins of Doriath. - The Silmarillion, Of the Sindar
These two quotes contradict each other, and LotR takes precedence. The important thing, which is mentioned in both, is that the dwarves value Daeron's work more than his own people do; and that they take something elven-made and make it into a fundamental part of their culture.
And thus it was that Caranthir's people came upon the Dwarves, who after the onslaught of Morgoth and the coming of the Noldor had ceased their traffic into Beleriand. But though either people loved skill and were eager to learn, no great love was there between them; for the Dwarves were secret and quick to resentment, and Caranthir was haughty and scarce concealed his scorn for the unloveliness of the Naugrim, and his people followed their lord. Nevertheless since both peoples feared and hated Morgoth they made alliance, and had of it great profit; for the Naugrim learned many secrets of craft in those days, so that the smiths and masons of Nogrod and Belegost became renowned among their kin, and when the Dwarves began again to journey into Beleriand all the traffic of the dwarf-mines passed first through the hands of Caranthir, and thus great riches came to him. - The Silmarillion, Of the Return of the Noldor
Caranthir's unpleasant personality is the reason there was no love between them. However, they had a very profitable business relationship.
Now on a time Finrod and Galadriel his sister were the guests of Thingol their kinsman in Doriath. Then Finrod was filled with wonder at the strength and majesty of Menegroth, its treasuries and armouries and its many-pillared halls of stone; and it came into his heart that he would build wide halls behind ever-guarded gates in some deep and secret place beneath the hills. Therefore he opened his heart to Thingol, telling him of his dreams; and Thingol spoke to him of the deep gorge of the River Narog, and the caves under the High Faroth in its steep western shore, and when he departed he gave him guides to lead him to that place of which few yet knew. Thus Finrod came to the Caverns of Narog, and began to establish there deep halls and armouries after the fashion of the mansions of Menegroth; and that stronghold was called Nargothrond. In that labour Finrod was aided by the Dwarves of the Blue Mountains; and they were rewarded well, for Finrod had brought more treasures out of Tirion than any other of the princes of the Noldor. And in that time was made for him the Nauglamír, the Necklace of the Dwarves, most renowned of their works in the Elder Days. It was a carcanet of gold, and set therein were gems uncounted from Valinor; but it had a power within it so that it rested lightly on its wearer as a strand of flax, and whatsoever neck it clasped it sat always with grace and loveliness. 
There in Nargothrond Finrod made his home with many of his people, and he was named in the tongue of the Dwarves Felagund, Hewer of Caves; and that name he bore thereafter until his end. - The Silmarillion, Of the Return of the Noldor 
Húrin made no answer to the King, but drew forth from beneath his cloak that one thing which he had taken with him out of Nargothrond; and that was no lesser treasure than the Nauglamír, the Necklace of the Dwarves, that was made for Finrod Felagund long years before by the craftsmen of Nogrod and Belegost, most famed of all their works in the Elder Days, and prized by Finrod while he lived above all the treasures of Nargothrond. - The Silmarillion, Of the Ruin of Doriath
This is an extremely important event that gets overlooked in most analysis'. It is made explicitly clear how prized and secret their names are to the dwarves:
Gimli's own name, however, and the names of all his kin, are of Northern (Mannish) origin. Their own secret and 'inner' names, their true names, the Dwarves have never revealed to anyone of alien race. Not even on their tombs do they inscribe them. - Lord of the Rings, Appendix F
And yet, these extremely secretive dwarves gave an elf a dwarvish name, to honor him. There must have been great friendship between Finrod and the dwarves, for this to happen. And, the mixture of elf and dwarf created another work of unparalleled beauty.
Few of the Eldar went ever to Nogrod and Belegost, save Eöl of Nan Elmoth and Maeglin his son;[cut]. - The Silmarillion, Of the Sindar 
But now the trees of Nan Elmoth were the tallest and darkest in all Beleriand, and there the sun never came; and there Eöl dwelt, who was named the Dark Elf. Of old he was of the kin of Thingol, but he was restless and ill at ease in Doriath, and when the Girdle of Melian was set about the Forest of Region where he dwelt he fled thence to Nan Elmoth. There he lived in deep shadow, loving the night and the twilight under the stars. He shunned the Noldor, holding them to blame for the return of Morgoth, to trouble the quiet of Beleriand; but for the Dwarves he had more liking than any other of the Elvenfolk of old. From him the Dwarves learned much of what passed in the lands of the Eldar. 
Now the traffic of the Dwarves down from the Blue Mountains followed two roads across East Beleriand, and the northern way, going towards the Fords of Aros, passed nigh to Nan Elmoth; and there Eöl would meet the Naugrim and hold converse with them. And as their friendship grew he would at times go and dwell as guest in the deep mansions of Nogrod or Belegost. There he learned much of metalwork, and came to great skill therein; and he devised a metal as hard as the steel of the Dwarves, but so malleable that he could make it thin and supple; and yet it remained resistant to all blades and darts. - The Silmarillion, Of Maeglin 
Often he went with Eöl to the cities of the Dwarves in the east of Ered Lindon, and there he learned eagerly what they would teach, and above all the craft of finding the ores of metals in the mountains. - The Silmarillion, Of Maeglin 
It came to pass that at the midsummer the Dwarves, as was their custom, bade Eöl to a feast in Nogrod; and he rode away. - The Silmarillion, Of Maeglin 
Therefore he said to Aredhel: “Lady, let us depart while there is time? What hope is there in this wood for you or for me? Here we are held in bondage, and no profit shall I find here; for I have learned all that my father has to teach, or that the Naugrim will reveal to me. Shall we not seek for Gondolin? You shall be my guide, and I will be your guard!” - The Silmarillion, Of Maeglin
Yes, Eöl and Maeglin are villains. However, they didn't show that to the dwarves. Instead, they were good friends. The dwarves even let Eöl dwell inside their realms, showing just how much they trusted and valued his friendship. However, even then the dwarves wouldn't reveal all their craft secrets.
But in truth this helm had not been made for Men, but for Azaghâl Lord of Belegost, he who was slain by Glaurung in the Year of Lamentation.4 It was given by Azaghâl to Maedhros, as guerdon for the saving of his life and treasure, when Azaghâl was waylaid by Orcs upon the Dwarf-road in East Beleriand.5 – Unfinished Tales, Narn i Hîn Húrin, The Departure of Túrin
Maedhros saves Azaghâl's life, and the thank you gift he gives Maedhros will become the famous Dragon-helm of Dor-lómin.
At length Maedhros, having gathered all the strength that he could of Elves and Men and Dwarves, resolved to assault Angband from east and west; and he purposed to march with banners displayed in open force over Anfauglith. - The Silmarillion, Of the Fifth Battle: Nirnaeth Arnoediad
A significant amount of dwarves answered Maedhros' call, and agreed to march in open war. Remember, the dwarves always got along better with the Noldor.
Yet fate saved the sons of Fëanor, and though all were wounded none were slain, for they drew together, and gathering a remnant of the Noldor and the Naugrim about them they hewed a way out of the battle and escaped far away towards Mount Dolmed in the east. 
Last of all the eastern force to stand firm were the Dwarves of Belegost, and thus they won renown. For the Naugrim withstood fire more hardily than either Elves or Men, and it was their custom moreover to wear great masks in battle hideous to look upon; and those stood them in good stead against the dragons. And but for them Glaurung and his brood would have withered all that was left of the Noldor. - The Silmarillion, Of the Fifth Battle: Nirnaeth Arnoediad
The dwarves are the only reason the Noldor survived the fifth battle. This almost certainly cemented the friendship between the dwarves and the sons of Fëanor.
For Mîm came of Dwarves that were banished in ancient days from the great Dwarf-cities of the east, and long before the return of Morgoth they wandered westward into Beleriand; but they became diminished in stature and in smith-craft, and they took to lives of stealth, walking with bowed shoulders and furtive steps. Before the Dwarves of Nogrod and Belegost came west over the mountains the Elves of Beleriand knew not what these others were, and they hunted them, and slew them; but afterwards they let them alone, and they were called Noegyth Nibin, the Petty-Dwarves, in the Sindarin tongue. They loved none but themselves, and if they feared and hated the Orcs, they hated the Eldar no less, and the Exiles most of all; for the Noldor, they said, had stolen their lands and their homes. Long ere King Finrod Felagund came over the Sea, the caves of Nargothrond were discovered by them, and by them its delving was begun; and beneath the crown of Amon Rûdh, the Bald Hill, the slow hands of the Petty-Dwarves had bored and deepened the caves through the long years that they dwelt there, untroubled by the Grey-elves of the woods. But now at last they had dwindled and died out of Middle-earth, all save Mîm and his two sons; and Mîm was old even in the reckoning of Dwarves, old and forgotten. And in his halls the smithies were idle, and the axes rusted, and their name was remembered only in ancient tales of Doriath and Nargothrond. - The Silmarillion, Of Túrin Turambar
Unlike the rest of their kin, the petty-dwarves disliked the Noldor most of all.
In those days the Dwarves still came on their journeys into Beleriand from their mansions in Ered Lindon, and passing over Gelion at Sam Athrad, the Ford of Stones, they travelled the ancient road to Doriath; for their skill in the working of metal and stone was very great, and there was much need of their craft in the halls of Menegroth. But they came now no longer in small parties as aforetime, but in great companies well armed for their protection in the perilous lands between Aros and Gelion; and they dwelt in Menegroth at such times in chambers and smithies set apart for them. At that very time great craftsmen of Nogrod were lately come into Doriath; and the King therefore summoning them declared his desire, that if their skill were great enough they should remake the Nauglamír, and in it set the Silmaril. Then the Dwarves looked upon the work of their fathers, and they beheld with wonder the shining jewel of Fëanor; and they were filled with a great lust to possess them, and carry them off to their far homes in the mountains. But they dissembled their mind, and consented to the task. - The Silmarillion, Of the Ruin of Doriath
Relations between the Sindar and dwarves was good enough for the dwarves to dwell comfortably in Menegroth. Though not close, the two races have had several centuries of friendship between them.

The dwarves said nothing about their desires, and agreed to take the job Thingol was offering.
Long was their labour; and Thingol went down alone to their deep smithies, and sat ever among them as they worked. In time his desire was achieved, and the greatest of the works of Elves and Dwarves were brought together and made one; and its beauty was very great, for now the countless jewels of the Nauglamír did reflect and cast abroad in marvellous hues the light of the Silmaril amidmost. Then Thingol, being alone among them, made to take it up and clasp it about his neck; but the Dwarves in that moment withheld it from him, and demanded that he yield it up to them, saying: 'By what right does the Elvenking lay claim to the Nauglamír, that was made by our fathers for Finrod Felagund who is dead? It has come to him but by the hand of Húrin the Man of Dor-lómin, who took it as a thief out of the darkness of Nargothrond.' But Thingol perceived their hearts, and saw well that desiring the Silmaril they sought but a pretext and fair cloak for their true intent; and in his wrath and pride he gave no heed to his peril, but spoke to them in scorn, saying: 'How do ye of uncouth race dare to demand aught of me, Elu Thingol, Lord of Beleriand, whose life began by the waters of Cuiviénen years uncounted ere the fathers of the stunted people awoke?' And standing tall and proud among them he bade them with shameful words be gone unrequited out of Doriath. - The Silmarillion, Of the Ruin of Doriath
The dwarves did not have the right to the Nauglamír. Nor should Thingol have gone immediately to scorn and insults.
Then the lust of the Dwarves was kindled to rage by the words of the King; and they rose up about him, and laid hands on him, and slew him as he stood. So died in the deep places of Menegroth Elwë Singollo, King of Doriath, who alone of all the Children of Ilúvatar was joined with one of the Ainur; and he who, alone of the Forsaken Elves, had seen the light of the Trees of Valinor, with his last sight gazed upon the Silmaril. - The Silmarillion, Of the Ruin of Doriath
There is no excuse that can make the dwarves' behavior acceptable.
Then the Dwarves taking the Nauglamír passed out of Menegroth and fled eastwards through Region. But tidings went swiftly through the forest, and few of that company came over Aros, for they were pursued to the death as they sought the eastward road; and the Nauglamír was retaken, and brought back in bitter grief to Melian the Queen. Yet two there were of the slayers of Thingol who escaped from the pursuit on the eastern marches, and returned at last to their city far off in the Blue Mountains; and there in Nogrod they told somewhat of all that had befallen, saying that the Dwarves were slain in Doriath by command of the Elvenking, who thus would cheat them of their reward. - The Silmarillion, Of the Ruin of Doriath
They killed Thingol, and then they lied to their kin. Not only did they lie, but they told their kin that Thingol committed the same type of crime they were guilty of.
Then great was the wrath and lamentation of the Dwarves of Nogrod for the death of their kin and their great craftsmen, and they tore their beards, and wailed; and long they sat taking thought for vengeance. It is told that they asked aid from Belegost, but it was denied them, and the Dwarves of Belegost sought to dissuade them from their purpose; but their counsel was unavailing, and ere long a great host came forth from Nogrod, and crossing over Gelion marched westward through Beleriand. - The Silmarillion, Of the Ruin of Doriath
It is important to note that not all dwarves agreed or participated in this senseless behavior.
Thus it was that the host of the Naugrim crossing over Aros passed unhindered into the woods of Doriath; and none withstood them, for they were many and fierce, and the captains of the Grey-elves were cast into doubt and despair, and went hither and thither purposeless. But the Dwarves held on their way, and passed over the great bridge, and entered into Menegroth; and there befell a thing most grievous among the sorrowful deeds of the Elder Days. For there was battle in the Thousand Caves, and many Elves and Dwarves were slain; and it has not been forgotten. But the Dwarves were victorious, and the halls of Thingol were ransacked and plundered. There fell Mablung of the Heavy Hand before the doors of the treasury wherein lay the Nauglamír; and the Silmaril was taken. - The Silmarillion, Of the Ruin of Doriath
Unhindered means “not slowed or blocked or interfered with”. Withstood means “to resist or oppose with determined effort”. Ransack means “to go through (a place) stealing valuables and causing disarray”. Plunder means “to seize wrongfully or by force”.

The elves did not fight the dwarves as they came, because they were too devastated by the loss of their King and Queen. The dwarves started the fight, and they continued to the heart of the realm. There is no doubt in my mind that elven civilians were killed by the dwarves. The elves killed some dwarves in self-defense; but the dwarves killed enough elves so that those remaining did not even dare try to stop the dwarves from destroying their home and taking whatever they wanted. Such a horrific act is understandably a source of great trauma and grief for the elves.
Now word went swiftly among the Elves of Ossiriand that a great host of Dwarves bearing gear of war had come down out of the mountains and passed over Gelion at the Ford of Stones. These tidings came soon to Beren and Lúthien; and in that time also a messenger came to them out of Doriath telling of what had befallen there. Then Beren arose and left Tol Galen, and summoning to him Dior his son they went north to the River Ascar; and with them went many of the Green-elves of Ossiriand. 
Thus it came to pass that when the Dwarves of Nogrod, returning from Menegroth with diminished host, came again to Sarn Athrad, they were assailed by unseen enemies; for as they climbed up Gelion's banks burdened with the spoils of Doriath, suddenly all the woods were filled with the sound of elven-horns, and shafts sped upon them from every side. There very many of the Dwarves were slain in the first onset; but some escaping from the ambush held together, and fled eastwards towards the mountains. And as they climbed the long slopes beneath Mount Dolmed there came forth the Shepherds of the Trees, and they drove the Dwarves into the shadowy woods of Ered Lindon: whence, it is said, came never one to climb the high passes that led to their homes. 
In that battle by Sarn Athrad Beren fought his last fight, and himself slew the Lord of Nogrod, and wrested from him the Necklace of the Dwarves; but he dying laid his curse upon all the treasure. Then Beren gazed in wonder on the selfsame jewel of Fëanor that he had cut from Morgoth's iron crown, now shining set amid gold and gems by the cunning of the Dwarves; and he washed it clean of blood in the waters of the river. And when all was finished the treasure of Doriath was drowned in the River Ascar, and from that time the river was named anew, Rathlóriel, the Goldenbed; but Beren took the Nauglamír and returned to Tol Galen. Little did it ease the grief of Lúthien to learn that the Lord of Nogrod was slain and many Dwarves beside; but it is said and sung that Lúthien wearing that necklace and that immortal jewel was the vision of greatest beauty and glory that has ever been outside the realm of Valinor; and for a little while the Land of the Dead that Live became like a vision of the land of the Valar, and no place has been since so fair, so fruitful, or so filled with light. - The Silmarillion, Of the Ruin of Doriath
The dwarves had taken a large amount of treasure with them, and they were not anticipating resistance.

The ents also knew how horrific the actions of the dwarves were, and they made sure justice was done.

We are now moving onto the Second Age.
After the end of the First Age the power and wealth of Khazad-dûm was much increased; for it was enriched by many people and much lore and craft when the ancient cities of Nogrod and Belegost in the Blue Mountains were ruined at the breaking of Thangorodrim. - Lord of the Rings, Appendix A, Durin's Folk
The survivors of the clan responsible for the horrific acts in Doriath merged with the dwarves in Moria, thereby bringing guilt of association. Before this, Durin and Moria were only a name to both the Sindar and the Noldor (see quote above).
But in far distant days the Dwarves were secretive [struck out: - and none more so than the Longbeards -] and had few dealings with the Elves. In the West at the end of the First Age the dealings of the Dwarves of the Ered Lindon with King Thingol ended in disaster and the ruin of Doriath, the memory of which still poisoned the relations of Elves and Dwarves in after ages. - The Peoples of Middle-earth, Of Dwarves and Men
This tells us that the ruin of Doriath will become the main contending point between the elves and dwarves.
This process began not in barter and trade, but in war; for the Longbeards had spread southward down the Vales of Anduin and had made their chief 'mansion' and stronghold at Moria; and also eastward to the Iron Hills, where the mines were their chief source of iron-ore. They regarded the Iron Hills, the Ered Mithrin, and the east dales of the Misty Mountains as their own land. But they were under attack from the Orks of Morgoth. During the War of the Jewels and the Siege of Angband, when Morgoth needed all his strength, these attacks ceased; but when Morgoth fell and Angband was destroyed hosts of the Orks fled eastwards seeking homes. They were now masterless and without any general leadership, but they were well-armed and very numerous, cruel, savage, and reckless in assault. In the battles that followed the Dwarves were outnumbered, and though they were the most redoubtable warriors of all the Speaking Peoples they were glad to make alliance with Men.(27) - The Peoples of Middle-earth, Of Dwarves and Men
This makes things very, very interesting. We know that early in the Second Age, a handful of anti-dwarf Sindar settled in Lórien and the southern part of the Greenwood; close to Moria. We also know that the two Sindarin kings were Oropher (Legolas's grandfather) and Amdír; and they were both princes of Doriath and close kin of Thingol (for more on this, see here).

So there is a very strong presence of dwarves, and said dwarves have alliances with the only humans in the region. This is a great recipe for conflict; which is hinted at.
She loved him indeed, for he was beautiful even for one of the Eldar, and valiant and wise; but she was of the Silvan Elves, and regretted the incoming of the Elves from the West, who (as she said) brought wars and destroyed the peace of old. She would speak only the Silvan tongue, even after it had fallen into disuse among the folk of Lórien;12 and she dwelt alone beside the falls of the river Nimrodel to which she gave her name. - Unfinished Tales, Part 2: The Second Age, 4: The History of Galadriel and Celeborn, Amroth and Nimrodel
Nimrodel is speaking in the early Third Age here, but no one can reasonably blame the War of the Last Alliance on anyone other than Sauron. We are also told that Lórien had no other contact with servants of the Dark Lord during the Second Age (see previous link). So, what conflicts is she referring to?
In the Second Age their king, Oropher [the father of Thranduil, father of Legolas], had withdrawn northward beyond the Gladden Fields. This he did to be free from the power and encroachments of the Dwarves of Moria, which had grown to be the greatest of the mansions of the Dwarves recorded in history; and also he resented the intrusions of Celeborn and Galadriel into Lórien. - Unfinished Tales, Part 2: The Second Age, 4: The History of Galadriel and Celeborn, Appendix B
Encroachment means “to intrude gradually, stealthily, or insidiously upon the rights, property, etc, of another.”

The dwarves of Moria were extremely powerful, and (in Oropher's view) intruding on the rights and lands of the elves'. Meanwhile, the dwarves regarded the non-forest surrounding areas as their own land.

While we are not told of any conflicts that happened, these quotes imply that there were some, and they certainly give more than enough reasoning for conflicts.

The dwarves of Moria were having much better relations with the Noldor, on the other side of the Misty Mountains:
Later some of the Noldor went to Eregion, upon the west of the Misty Mountains, and near to the West-gate of Moria. This they did because they learned that mithril had been discovered in Moria.4 The Noldor were great craftsmen and less unfriendly to the Dwarves than the Sindar; but the friendship that grew up between the people of Durin and the Elven-smiths of Eregion was the closest that there has ever been between the two races. - Lord of the Rings, Appendix B, The Second Age 
But Moria is an Elvish name, and given without love; for the Eldar, though they might at need, in their bitter wars with the Dark Power and his servants, contrive fortresses underground, were not dwellers in such places of choice. They were lovers of the green earth and the lights of heaven; and Moria in their tongue means the Black Chasm. - Lord of the Rings, Appendix F, On Translation 
Eregion was nigh to the great mansions of the Dwarves that were named Khazad-dûm, but by the Elves Hadhodrond, and afterwards Moria. From Ost-in-Edhil, the city of the Elves, the highroad ran to the west gate of Khazad-dûm, for a friendship arose between Dwarves and Elves, such as has never elsewhere been, to the enrichment of both those peoples. - The Silmarillion, Of the Rings of Power and the Third Age
The Noldor first moved to Eregion for business (mithril), but they then made a great and unexpected friendship with the dwarves.

The part from The Silmarillion, of the elves calling Moria, Hadhodrond is contradicted by LotR. We know, from the chapter A Journey in the Dark, that 'Moria' was the word the elves put on the door. Even though they had a great and true friendship, the elves still named Moria 'Black Chasm', because the idea of voluntarily living underground seemed abhorrent to them. It was not because of the dwarves themselves.
The Dwarves were not, however, skilled linguists - in most matters they were unadaptable - and spoke with a marked 'dwarvish' accent. Also they had never invented any form of alphabetic writing.(5) They quickly, however, recognized the usefulness of the Elvish systems, when they at last became sufficiently friendly with any of the Eldar to learn them. This occurred mainly in the close association of Eregion and Moria in the Second Age. Now in Eregion not only the Fëanorian Script, which had long become a mode of writing generally used (with various adaptations) among all 'lettered' peoples in contact with the Numenorean settlements,(6) but also the ancient 'runic' alphabet of Daeron elaborated [> used] by the Sindar was known and used. 
The Longbeard Dwarves therefore adopted the Runes, and modified them for their own uses (especially the expression of Khuzdul); and they adhered to them even far into the Third Age, when they were forgotten by others except the loremasters of Elves and Men. Indeed it was generally supposed by the unlearned that they had been invented by the Dwarves, and they were widely known as 'dwarf-letters'.(8) 
8. They did not, however, appear in the inscriptions on the West Gate of Moria. The Dwarves said that it was in courtesy to the Elves that the Fëanorian letters were used on that gate, since it opened into their country and was chiefly used by them. But the East Gates, which perished in the war against the Orks, had opened upon the wide world, and were less friendly. They had borne Runic inscriptions in several tongues: spells of prohibition and exclusion in Khuzdul, and commands that all should depart who had not the leave of the Lord of Moria written in Quenya, Sindarin, the Common Speech, the languages of Rohan and of Dale and Dunland. - The Peoples of Middle-earth, Of Dwarves and Men
I quoted and talked above, about the dwarves' use of Daeron's work. This is when the dwarves learned of it; as the Noldor had taken knowledge of it with them to Eregion.

The elves' and dwarves' friendship was great enough that they gave the elves their own personal door into Moria.
They had however been much mingled with Noldor (of Sindarin speech), who passed through Moria after the destruction of Eregion by Sauron in the year 1697 of the Second Age. At that time Elrond went westward [sic; probably meaning simply that he did not cross Misty Mountains] and established the refuse of Imladris; Celeborn went at first to Lórien and fortified it against any further attempts of Sauron to cross the Anduin. When however Sauron withdrew to Mordor, and was (as reported) wholly concerned with conquests in the East, Celeborn rejoined Galadriel in Lindon. 
The implication of the extract just given is that after Eregion's fall Celeborn led this migration to Lórien, while Galadriel joined Gil-galad in Lindon; but elsewhere, in a writing contemporary with this, it is said explicitly that they both at that time “passed through Moria with a considerable following of Noldorin exiles and dwelt for many years in Lórien.” - Unfinished Tales, Part 2: The Second Age, 4: The History of Galadriel and Celeborn, Amroth and Nimrodel
Either Celeborn, or Celeborn and Galadriel, led the migration through Moria to Lórien. It is notable that the dwarves allowed and supported the elves in doing this.
All living things were divided in that day, and some of every kind, even of beasts and birds, were found in either host, save the Elves only. They alone were undivided and followed Gil- galad. Of the Dwarves few fought upon either side; but the kindred of Durin of Moria fought against Sauron. - The Silmarillion, Of the Rings of Power and the Third Age
The elves may have held it against the dwarves that some of their kin fought for Sauron.
But in the Third Age something of their old character and power is still glimpsed, if already a little dimmed: these are the descendants of the Naugrim of the Elder Days, in whose hearts still burns the ancient fire of Aulë the Smith, and the embers smoulder of their long grudge against the Elves; and in whose hands still lives the skill in works of stone that none have surpassed. - Lord of the Rings, Appendix F
The dwarves have not forgotten their grudge over the events of Doriath.
TA 1980: A Balrog appears in Moria, and slays Durin VI. 
TA 1981: Náin I slain. The Dwarves flee from Moria. Many of the Silvan Elves of Lórien flee south. Amroth and Nimrodel are lost. - Lord of the Rings, Appendix B 
But when the terror came out of Moria and the Dwarves were driven out, and in their stead Orcs crept in, she fled distraught alone south into empty lands [in the year 1981 of the Third Age]. 
After the disaster in Moria [in the year 1980] and the sorrows of Lórien, which was now left without a ruler (for Amroth was drowned in the sea in the Bay of Belfalas and left no heir), Celeborn and Galadriel returned to Lórien, and were welcomed by the people. 
Nevertheless, it was not until the disaster in Moria, when by means is beyond the foresight of Galadriel Sauron's power actually crossed the Anduin and Lórien was in great peril, its king lost, its people fleeing and likely to leave it deserted to likely occupied by Orcs, that Galadriel and Celeborn took up their permanent abode in Lórien, and its government. - Unfinished Tales, Part 2: The Second Age, 4: The History of Galadriel and Celeborn, Amroth and Nimrodel
Lórien and its people were greatly effected by the Balrog and subsequent orcs.
“You have had some very strange adventures, I hear,” said Glóin. “I wonder greatly what brings four hobbits on so long a journey. Nothing like it has happened since Bilbo came with us. But perhaps I should not inquire too closely, since Elrond and Gandalf do not seem disposed to talk of this?” 
“I think we will not speak of it, at least not yet,” said Frodo politely. 
He guessed that even in Elrond's house the matter of the Ring was not one for casual talk; and in any case he wished to forget his troubles for a time. “But I am equally curious,” he added, “to learn what brings so important a dwarf so far from the Lonely Mountain.” 
Glóin looked at him. “If you have not heard, I think we will not speak yet of that either. Master Elrond will summon us all ere long, I believe, and then we shall all hear many things. But there is much else that may be told.” 
A shadow passed over Glóin's face. “We do not know,” he answered. “It is largely on account of Balin that I have come to ask the advice of those that dwell in Rivendell. But tonight let us speak of merrier things!” - Lord of the Rings, Many Meetings
Glóin is civil when speaking about Elrond and the elves of Rivendell.
Of these things Frodo had already heard many rumours; but the tale of Glóin was new to him, and when the dwarf spoke he listened attentively. It appeared that amid the splendour of their works of hand the hearts of the Dwarves of the Lonely Mountain were troubled. 
“It is now many years ago,” said Glóin, “that a shadow of disquiet fell upon our people. Whence it came we did not at first perceive. Words began to be whispered in secret: it was said that we were hemmed in a narrow place, and that greater wealth and splendour would be found in a wider world. Some spoke of Moria: the mighty works of our fathers that are called in our own tongue Khazad-dûm; and they declared that now at last we had the power and numbers to return.” 
Glóin sighed. “Moria! Moria! Wonder of the Northern world! Too deep we delved there, and woke the nameless fear. Long have its vast mansions lain empty since the children of Durin fled. But now we spoke of it again with longing, and yet with dread; for no dwarf has dared to pass the doors of Khazad-dûm for many lives of kings, save Thrór only, and he perished. At last, however, Balin listened to the whispers, and resolved to go; and though Dáin did not give leave willingly, he took with him Ori and Óin and many of our folk, and they went away south. 
That was nigh on thirty years ago. For a while we had news and it seemed good: messages reported that Moria had been entered and a great work begun there. Then there was silence, and no word has ever come from Moria since. 
Then about a year ago a messenger came to Dáin, but not from Moria - from Mordor: a horseman in the night, who called Dáin to his gate. The Lord Sauron the Great, so he said, wished for our friendship. Rings he would give for it, such as he gave of old. And he asked urgently concerning hobbits, of what kind they were, and where they dwelt. “For Sauron knows,” said he, “that one of these was known to you on a time.” 
At this we were greatly troubled, and we gave no answer. And then his fell voice was lowered, and he would have sweetened it if he could. “As a small token only of your friendship Sauron asks this,” he said: “that you should find this thief,” such was his word, “and get from him, willing or no, a little ring, the least of rings, that once he stole. It is but a trifle that Sauron fancies, and an earnest of your good will. Find it, and three rings that the Dwarf sires possessed of old shall be returned to you, and the realm of Moria shall be yours for ever. Find only news of the thief, whether he still lives and where, and you shall have great reward and lasting friendship from the Lord. Refuse, and things will not seem so well. Do you refuse?” 
At that his breath came like the hiss of snakes, and all who stood by shuddered, but Dáin said: “I say neither yea nor nay. I must consider this message and what it means under its fair cloak.” 
“Consider well, but not too long,” said he. 
“The time of my thought is my own to spend,” answered Dáin. 
“For the present,” said he, and rode into the darkness. 
Heavy have the hearts of our chieftains been since that night. We needed not the fell voice of the messenger to warn us that his words held both menace and deceit; for we knew already that the power that has re-entered Mordor has not changed, and ever it betrayed us of old. Twice the messenger has returned, and has gone unanswered. The third and last time, so he says, is soon to come, before the ending of the year. 
And so I have been sent at last by Dáin to warn Bilbo that he is sought by the Enemy, and to learn, if may be, why he desires this ring, this least of rings. Also we crave the advice of Elrond. For the Shadow grows and draws nearer. We discover that messengers have come also to King Brand in Dale, and that he is afraid. We fear that he may yield. Already war is gathering on his eastern borders. If we make no answer, the Enemy may move Men of his rule to assail King Brand, and Dáin also.” - Lord of the Rings, The Council of Elrond
The dwarves are not friendly with the elves of Rivendell, but they are civil. They must know Bilbo has been living in Rivendell for many years, and they recognize Elrond's wisdom. Glóin does not hold back any details from the Council.
Gandalf: “The Seven are taken or destroyed.” At this Glóin stirred, but did not speak. - Lord of the Rings, The Council of Elrond
Glóin is startled by Gandalf's statement, but does not interrupt him.
“You were less tender to me,” said Glóin with a flash of his eyes as old memories were stirred of his imprisonment in the deep places of the Elven-king's halls. 
“Now come!” said Gandalf. “Pray do not interrupt, my good Glóin. That was a regrettable misunderstanding, long set right. If all the grievances that stand between Elves and Dwarves are to be brought up here, we may as well abandon this Council.” 
Glóin rose and bowed, and Legolas continued. - Lord of the Rings, The Council of Elrond
As we went over, the dwarves have a much better history with the Noldor than with the Sindar. In this case, the elves of Rivendell versus the elves of Mirkwood. Glóin interrupts and brings up his enmity with the elves of Mirkwood, making it clear that the past conflicts have not been forgotten. Also, the fact that Glóin interrupts Legolas about this when he didn't interrupt Gandalf about the Seven says a lot.
“Still it might be well for all,” said Glóin the Dwarf, “if all these strengths were joined, and the powers of each were used in league. Other rings there may be, less treacherous, that might be used in our need. The Seven are lost to us - if Balin has not found the ring of Thrór which was the last; naught has been heard of it since Thrór perished in Moria. Indeed I may now reveal that it was partly in hope to find that ring that Balin went away.” 
“Balin will find no ring in Moria,” said Gandalf. “Thrór gave it to Thráin his son, but not Thráin to Thorin. It was taken with torment from Thráin in the dungeons of Dol Guldur. I came too late.” 
“Ah, alas!” cried Glóin. “When will the day come of our revenge? But still there are the Three. What of the Three Rings of the Elves? Very mighty Rings, it is said. Do not the Elf-lords keep them? Yet they too were made by the Dark Lord long ago. Are they idle? I see Elf-lords here. Will they not say?” 
The Elves returned no answer. “Did you not hear me, Glóin?” said Elrond. 
“But what then would happen, if the Ruling Ring were destroyed as you counsel?” asked Glóin. - Lord of the Rings, The Council of Elrond
Glóin pushes the matter of the Three. However, he is civil in listening and asking questions.
At that moment Elrond came out with Gandalf, and he called the Company to him. “This is my last word,” he said in a low voice. “The Ring-bearer is setting out on the Quest of Mount Doom. On him alone is any charge laid: neither to cast away the Ring, nor to deliver it to any servant of the Enemy nor indeed to let any handle it, save members of the Company and the Council, and only then in gravest need. The others go with him as free companions, to help him on his way. You may tarry, or come back, or turn aside into other paths, as chance allows. The further you go, the less easy will it be to withdraw; yet no oath or bond is laid on you to go further than you will. For you do not yet know the strength of your hearts, and you cannot foresee what each may meet upon the road.” 
“Faithless is he that says farewell when the road darkens,” said Gimli. 
“Maybe,” said Elrond, “but let him not vow to walk in the dark, who has not seen the nightfall.” 
“Yet sworn word may strengthen quaking heart,” said Gimli. 
“Or break it,” said Elrond. - Lord of the Rings, The Ring Goes South
In his wisdom, Elrond cautions Gimli about oath making. Elrond's words hint at the tragic tales of the Silmarillion.
“Well, here we are at last!” said Gandalf. “Here the Elven-way from Hollin ended. Holly was the token of the people of that land, and they planted it here to mark the end of their domain; for the West-door was made chiefly for their use in their traffic with the Lords of Moria. Those were happier days, when there was still close friendship at times between folk of different race, even between Dwarves and Elves.” 
“It was not the fault of the Dwarves that the friendship waned,” said Gimli. 
“I have not heard that it was the fault of the Elves,” said Legolas. 
“I have heard both,” said Gandalf; “and I will not give judgement now. But I beg you two, Legolas and Gimli, at least to be friends, and to help me. I need you both. The doors are shut and hidden, and the sooner we find them the better. Night is at hand!” - Lord of the Rings, A Journey in the Dark
The Company arrives at Moria, and Gandalf mentions the “close friendship” the elves and dwarves there had. Gimli buts in, insisting that the dwarves are blameless. Legolas then gets defensive and insists that the elves are blameless. Gandalf says he has heard both sides, and stops the fight from escalating further.

It is not clear what events they are referring to, since this friendship took place after Doriath. They are likely talking in a general sense.
“There are the emblems of Durin!” cried Gimli. 
“And there is the Tree of the High Elves!” said Legolas. 
“And the Star of the House of Fëanor,” said Gandalf. “They are wrought of ithildin that mirrors only starlight and moonlight, and sleeps until it is touched by one who speaks words now long forgotten in Middle-earth. It is long since I heard them, and I thought deeply before I could recall them to my mind.” 
“What does the writing say?” asked Frodo, who was trying to decipher the inscription on the arch. “I thought I knew the elf-letters but I cannot read these.” 
“The words are in the elven-tongue of the West of Middle-earth in the Elder Days,” answered Gandalf. “But they do not say anything of importance to us. They say only: The Doors of Durin, Lord of Moria. Speak, friend, and enter. And underneath small and faint is written: I, Narvi, made them. Celebrimbor of Hollin drew these signs.” - Lord of the Rings, A Journey in the Dark
We went over above how the two realms had a great and true friendship. The dwarves greatly honored their friends by combining both groups' sacred symbols.
“Yes,” said Gandalf, “these doors are probably governed by words. Some dwarf-gates will open only at special times, or for particular persons; and some have locks and keys that are still needed when all necessary times and words are known. These doors have no key. In the days of Durin they were not secret. They usually stood open and doorwards sat here. But if they were shut, any who knew the opening word could speak it and pass in. At least so it is recorded, is it not, Gimli?” - Lord of the Rings, A Journey in the Dark
The dwarves' kept the elves' personal door to their realm open and guarded. This is just one more thing that shows how close the two realms were.
“I was wrong after all,” said Gandalf, “and Gimli too. Merry, of all people, was on the right track. The opening word was inscribed on the archway all the time! The translation should have been: Say “Friend” and enter. I had only to speak the Elvish word for friend and the doors opened. Quite simple. Too simple for a learned lore-master in these suspicious days. Those were happier times. Now let us go!” - Lord of the Rings, A Journey in the Dark
The two realms truly had a great friendship.
“These are not holes,” said Gimli. “This is the great realm and city of the Dwarrowdelf. And of old it was not darksome, but full of light and splendour, as is still remembered in our songs.” 
He rose and standing in the dark he began to chant in a deep voice, while the echoes ran away into the roof.
“The world was young, the mountains green, 
No stain yet on the Moon was seen, 
No words were laid on stream or stone 
When Durin woke and walked alone. 
He named the nameless hills and dells; 
He drank from yet untasted wells; 
He stooped and looked in Mirrormere, 
And saw a crown of stars appear, 
As gems upon a silver thread, 
Above the shadow of his head. 
The world was fair, the mountains tall, 
In Elder Days before the fall 
Of mighty kings in Nargothrond 
And Gondolin, who now beyond 
The Western Seas have passed away: 
The world was fair in Durin's Day. 
A king he was on carven throne 
In many-pillared halls of stone 
With golden roof and silver floor, 
And runes of power upon the door. 
The light of sun and star and moon 
In shining lamps of crystal hewn 
Undimmed by cloud or shade of night 
There shone for ever fair and bright. 
There hammer on the anvil smote, 
There chisel clove, and graver wrote; 
There forged was blade, and bound was hilt; 
The delver mined, the mason built. 
There beryl, pearl, and opal pale, 
And metal wrought like fishes' mail, 
Buckler and corslet, axe and sword, 
And shining spears were laid in hoard. 
Unwearied then were Durin's folk 
Beneath the mountains music woke: 
The harpers harped, the minstrels sang, 
And at the gates the trumpets rang. 
The world is grey, the mountains old, 
The forge's fire is ashen-cold 
No harp is wrung, no hammer falls: 
The darkness dwells in Durin's halls 
The shadow lies upon his tomb 
In Moria, in Khazad-dûm. 
But still the sunken stars appear 
In dark and windless Mirrormere; 
There lies his crown in water deep, 
Till Durin wakes again from sleep.” - Lord of the Rings, A Journey in the Dark
The dwarves' friendship with the elves was so great that they lamented the loss of the Noldor and even include the somewhat insulting name of 'Moria' in their song honoring their lost home and past.
“For mithril,” answered Gandalf. “The wealth of Moria was not in gold and jewels, the toys of the Dwarves; nor in iron, their servant. Such things they found here, it is true, especially iron; but they did not need to delve for them: all things that they desired they could obtain in traffic. For here alone in the world was found Moria-silver, or true-silver as some have called it: mithril is the Elvish name. The Dwarves have a name which they do not tell. Its worth was ten times that of gold, and now it is beyond price; for little is left above ground, and even the Orcs dare not delve here for it. The lodes lead away north towards Caradhras, and down to darkness. The Dwarves tell no tale; but even as mithril was the foundation of their wealth, so also it was their destruction: they delved too greedily and too deep, and disturbed that from which they fled, Durin's Bane. Of what they brought to light the Orcs have gathered nearly all, and given it in tribute to Sauron, who covets it. 
Mithril! All folk desired it. It could be beaten like copper, and polished like glass; and the Dwarves could make of it a metal, light and yet harder than tempered steel. Its beauty was like to that of common silver, but the beauty of mithril did not tarnish or grow dim. The Elves dearly loved it, and among many uses they made of it ithildin, starmoon, which you saw upon the doors. Bilbo had a corslet of mithril-rings that Thorin gave him. I wonder what has become of it? Gathering dust still in Michel Delving Mathom-house, I suppose.” - Lord of the Rings, A Journey in the Dark
Gandalf gives us more history on mithril and Moria.
“These are Daeron's Runes, such as were used of old in Moria,” said Gandalf. “Here is written in the tongues of Men and Dwarves: 
balin son of fundin 
lord of moria.” - Lord of the Rings, A Journey in the Dark
We went over the history of Daeron's Runes above. Here we see them used.
Frodo and Gimli standing at his side could see, as he gingerly turned the leaves, that they were written by many different hands, in runes, both of Moria and of Dale, and here and there in Elvish script. - Lord of the Rings, The Bridge of Khazad-dûm
Ori used both Daeron's Runes and Tengwar.
The others followed; but Gimli had to be dragged away by Legolas: in spite of the peril he lingered by Balin's tomb with his head bowed. - Lord of the Rings, The Bridge of Khazad-dûm
Even though Legolas and Gimli are not friends, Legolas still cares about Gimli's life.
“Lothlórien!” said Aragorn. “Glad I am to hear again the wind in the trees! We are still little more than five leagues from the Gates, but we can go no further. Here let us hope that the virtue of the Elves will keep us tonight from the peril that comes behind.” 
“If Elves indeed still dwell here in the darkening world,” said Gimli. 
“It is long since any of my own folk journeyed hither back to the land whence we wandered in ages long ago,” said Legolas, “but we hear that Lórien is not yet deserted, for there is a secret power here that holds evil from the land. Nevertheless its folk are seldom seen, and maybe they dwell now deep in the woods and far from the northern border.” 
“Indeed deep in the wood they dwell,” said Aragorn, and sighed as if some memory stirred in him. - Lord of the Rings, Lothlórien
Gimli questions if the elves of Lothlórien are still around, and Legolas responds with what he knows. Aragorn confirms Legolas's guess.
The voice of Legolas faltered, and the song ceased. “I cannot sing any more,” he said. “That is but a part, for I have forgotten much. It is long and sad, for it tells how sorrow came upon Lothlórien, Lórien of the Blossom, when the Dwarves awakened evil in the mountains.” 
“But the Dwarves did not make the evil,” said Gimli. 
“I said not so; yet evil came,” answered Legolas sadly. - Lord of the Rings, Lothlórien
Legolas continues to be civil, and does not blame the dwarves for what they did not create. Of course, this happens after their encounter with the Balrog, so we don't know what Legolas thought before that.
“The name of Aragorn son of Arathorn is known in Lórien,” said Haldir, “and he has the favour of the Lady. All then is well. But you have yet spoken only of seven.” 
“The eighth is a dwarf,” said Legolas. 
A dwarf!” said Haldir. “That is not well. We have not had dealings with the Dwarves since the Dark Days. They are not permitted in our land. I cannot allow him to pass.” 
“But he is from the Lonely Mountain, one of Dáin's trusty people, and friendly to Elrond,” said Frodo. “Elrond himself chose him to be one of our companions, and he has been brave and faithful.” 
The Elves spoke together in soft voices, and questioned Legolas in their own tongue. “Very good,” said Haldir at last. “We will do this, though it is against our liking. If Aragorn and Legolas will guard him, and answer for him, he shall pass; but he must go blindfold through Lothlórien. 
But now we must debate no longer. Your folk must not remain on the ground. We have been keeping watch on the rivers, ever since we saw a great troop of Orcs going north toward Moria, along the skirts of the mountains, many days ago. Wolves are howling on the wood's borders. If you have indeed come from Moria, the peril cannot be far behind. Tomorrow early you must go on. 
The four hobbits shall climb up here and stay with us - we do not fear them! There is another talan in the next tree. There the others must take refuge. You, Legolas, must answer to us for them. Call us, if anything is amiss! And have an eye on that dwarf!” - Lord of the Rings, Lothlórien
Legolas hesitates to say they have a dwarf in their Company, and does not defend Gimli to Haldir. He does answer Haldir's questions.

Haldir is greatly dismayed by Gimli's presence, referring to a period of time they call “the Dark Days”. He debates for a while and only then reluctantly agrees to shelter Gimli, when the only other option for him is death by creatures of evil. Haldir also insists that Gimli be blindfolded and guarded by Legolas and Aragorn – the only two members of the Company the elves trust. It is clear that the elves of Lothlórien greatly dislike and distrust dwarves.
“Now, friends,” said Haldir, “you have entered the Naith of Lórien or the Gore, as you would say, for it is the land that lies like a spear-head between the arms of Silverlode and Anduin the Great. We allow no strangers to spy out the secrets of the Naith. Few indeed are permitted even to set foot there. 
As was agreed, I shall here blindfold the eyes of Gimli the Dwarf. The other may walk free for a while, until we come nearer to our dwellings, down in Egladil, in the Angle between the waters.” 
This was not at all to the liking of Gimli. “The agreement was made without my consent,” he said. “I will not walk blindfold, like a beggar or a prisoner. And I am no spy. My folk have never had dealings with any of the servants of the Enemy. Neither have we done harm to the Elves. I am no more likely to betray you than Legolas, or any other of my companions.” 
“I do not doubt you,” said Haldir. “Yet this is our law. I am not the master of the law, and cannot set it aside. I have done much in letting you set foot over Celebrant.” - Lord of the Rings, Lothlórien
Gimli is not correct in stating that his people have never harmed elves, but that is certainly their point of view on the matter. Haldir does not argue, but states the elves' law. The others will also have to be blindfolded later.
Gimli was obstinate. He planted his feet firmly apart, and laid his hand upon the haft of his axe. “I will go forward free,” he said, “or I will go back and seek my own land, where I am known to be true of word, though I perish alone in the wilderness.” 
“You cannot go back,” said Haldir sternly. “Now you have come thus far, you must be brought before the Lord and the Lady. They shall judge you, to hold you or to give you leave, as they will. You cannot cross the rivers again, and behind you there are now secret sentinels that you cannot pass. You would be slain before you saw them.” 
Gimli drew his axe from his belt. Haldir and his companion bent their bows. “A plague on Dwarves and their stiff necks!” said Legolas. 
“Come!” said Aragorn. “If I am still to lead this Company, you must do as I bid. It is hard upon the Dwarf to be thus singled out. We will all be blindfold, even Legolas. That will be best, though it will make the journey slow and dull.” 
Gimli laughed suddenly. “A merry troop of fools we shall look! Will Haldir lead us all on a string, like many blind beggars with one dog? But I will be content, if only Legolas here shares my blindness.” 
“I am an Elf and a kinsman here,” said Legolas, becoming angry in his turn. 
“Now let us cry: “a plague on the stiff necks of Elves!”” said Aragorn. “But the Company shall all fare alike. Come, bind our eyes Haldir!” 
“I shall claim full amends for every fall and stubbed toe, if you do not lead us well,” said Gimli as they bound a cloth about his eyes. 
“You will have no claim,” said Haldir. “I shall lead you well, and the paths are smooth and straight.” - Lord of the Rings, Lothlórien
Legolas has no sympathy for Gimli, and instead gets angry at his resistance to being blindfolded. He even says that he wishes ill on proud and stubborn dwarves. Aragorn tries to keep the peace, but Gimli continues the fight; calling Haldir a dog and singling out Legolas. Legolas, of course, just gets angrier. Aragorn takes charge and ends the fight before it can continue any further.

Gimli then threatens Haldir with vengeance. Haldir, thankfully, stays civil and calm.
“Also,” said Haldir, “they bring me a message from the Lord and Lady of the Galadhrim. You are all to walk free, even the dwarf Gimli. It seems that the Lady knows who and what is each member of your Company. New messages have come from Rivendell perhaps.” 
He removed the bandage first from Gimli's eyes. “Your pardon!” he said, bowing low. “Look on us now with friendly eyes! Look and be glad, for you are the first dwarf to behold the trees of the Naith of Lórien since Durin's Day!- Lord of the Rings, Lothlórien
Messages arrive that no one should be blindfolded.

We now find out when the Dark Days were – after the Balrog awoke and Durin died. We went over this dark period above.
Celeborn: “Welcome Gimli son of Glóin! It is long indeed since we saw one of Durin's folk in Caras Galadhon. But today we have broken our long law. May it be a sign that though the world is now dark better days are at hand, and that friendship shall be renewed between our peoples.” Gimli bowed low. 
“Alas!” said Aragorn. “Gandalf the Grey fell into shadow. He remained in Moria and did not escape.” 
At these words all the Elves in the hall cried aloud in grief and amazement. “These are evil tidings,” said Celeborn, “the most evil that have been spoken here in long years full of grievous deeds.” 
“Indeed I saw upon the bridge that which haunts our darkest dreams, I saw Durin's Bane,” said Gimli in a low voice, and dread was in his eyes. 
“Alas!” said Celeborn. “We long have feared that under Caradhras a terror slept. But had I known that the Dwarves had stirred up this evil in Moria again, l would have forbidden you to pass the northern borders, you and all that went with you. And if it were possible, one would say that at the last Gandalf fell from wisdom into folly, going needlessly into the net of Moria.” - The Lord of the Rings, The Mirror of Galadriel
Celeborn stars out with words of friendship and hope, and Gimli responds with a respectful bow. Then, like everyone else, Celeborn is horrified by news of Gandalf's death. He instinctively reacts and blames Gimli, because it was Gimli's people who woke the Balrog.
“He would be rash indeed that said that thing,” said Galadriel gravely. “Needless were none of the deeds of Gandalf in life. Those that followed him knew not his mind and cannot report his full purpose. But however it may be with the guide, the followers are blameless. Do not repent of your welcome to the Dwarf. If our folk had been exiled long and far from Lothlórien, who of the Galadhrim, even Celeborn the Wise, would pass nigh and would not wish to look upon their ancient home, though it had become an abode of dragons? 
Dark is the water of Kheled-zâram, and cold are the springs of Kibil-nâla, and fair were the many-pillared halls of Khazad-dûm in Elder Days before the fall of mighty kings beneath the stone.” She looked upon Gimli, who sat glowering and sad, and she smiled. And the Dwarf, hearing the names given in his own ancient tongue, looked up and met her eyes; and it seemed to him that he looked suddenly into the heart of an enemy and saw there love and understanding. Wonder came into his face, and then he smiled in answer. 
He rose clumsily and bowed in dwarf-fashion, saying: “Yet more fair is the living land of Lórien, and the Lady Galadriel is above all the jewels that lie beneath the earth!” 
There was a silence. At length Celeborn spoke again. “I did not know that your plight was so evil,” he said. “Let Gimli forget my harsh words: I spoke in the trouble of my heart. I will do what I can to aid you, each according to his wish and need, but especially that one of the little folk who bears the burden.” - The Lord of the Rings, The Mirror of Galadriel
Celeborn somewhat apologizes, takes back his harsh words that were spoken out of fear, and promises to help in whatever way he can.

Now, Galadriel and Gimli. This scene is crucial to understanding their relationship. She gives him love, kindness, and understanding. Gimli is awed by both her actions and her, declaring that Lórien is more beautiful than Moria and that she is greater than the dwarves' beloved jewels. This is the beginning of his deep love for her.
Legolas was away much among the Galadhrim, and after the first night he did not sleep with the other companions, though he returned to eat and talk with them. Often he took Gimli with him when he went abroad in the land, and the others wondered at this change. - The Lord of the Rings, The Mirror of Galadriel
This is the beginning of Legolas's and Gimli's friendship. While they certainly have a great friendship, it is not like how it's usually portrayed in the fandom. Legolas has a deeper bond with Aragorn (see here), and it takes Gimli's drastic change of heart and deep love for Galadriel for Legolas to see him as a potential friend.
Gimli took up one of the cakes and looked at it with a doubtful eye. 
Cram,” he said under his breath, as he broke off a crisp corner and nibbled at it. His expression quickly changed, and he ate all the rest of the cake with relish. 
“No more, no more!” cried the Elves laughing. “You have eaten enough already for a long day's march.” 
“I thought it was only a kind of cram, such as the Dale-men make for journeys in the wild,” said the Dwarf. 
“So it is,” they answered. “But we call it lembas or waybread, and it is more strengthening than any food made by Men, and it is more pleasant than cram, by all accounts.” 
“Indeed it is,” said Gimli. “Why it is better than the honey-cakes of the Beornings, and that is great praise, for the Beornings are the best bakers that I know of; but they are none too willing to deal out their cakes to travellers in these days. You are kindly hosts!” 
“All the same, we bid you spare the food,” they said. - Lord of the Rings, Farewell to Lórien
Gimli and the elves are open and friendly with each other.
The Company was arranged in this way: Aragorn, Frodo, and Sam were in one boat; Boromir, Merry, and Pippin in another; and in the third were Legolas and Gimli, who had now become fast friends. - Lord of the Rings, Farewell to Lórien
Fast friends means “good, loyal friends.” Legolas and Gimli have looked past their prejudices and become good friends.
“And what gift would a Dwarf ask of the Elves?” said Galadriel turning to Gimli. 
None, Lady,” answered Gimli. “It is enough for me to have seen the Lady of the Galadhrim, and to have heard her gentle words.” 
“Hear all ye Elves!” she cried to those about her. “Let none say again that Dwarves are grasping and ungracious! Yet surely, Gimli son of Glóin, you desire something that I could give? Name it, I bid you! You shall not be the only guest without a gift.” 
“There is nothing, Lady Galadriel,” said Gimli, bowing low and stammering. “Nothing, unless it might be - unless it is permitted to ask, nay, to name a single strand of your hair, which surpasses the gold of the earth as the stars surpass the gems of the mine. I do not ask for such a gift. But you commanded me to name my desire.” 
The Elves stirred and murmured with astonishment, and Celeborn gazed at the Dwarf in wonder, but the Lady smiled. “It is said that the skill of the Dwarves is in their hands rather than in their tongues,” she said; “yet that is not true of Gimli. For none have ever made to me a request so bold and yet so courteous. And how shall I refuse, since I commanded him to speak? But tell me, what would you do with such a gift?” 
Treasure it, Lady,” he answered, “in memory of your words to me at our first meeting. And if ever I return to the smithies of my home, it shall be set in imperishable crystal to be an heirloom of my house, and a pledge of good will between the Mountain and the Wood until the end of days.” 
Then the Lady unbraided one of her long tresses, and cut off three golden hairs, and laid them in Gimli's hand. “These words shall go with the gift,” she said. “I do not foretell, for all foretelling is now vain: on the one hand lies darkness, and on the other only hope. But if hope should not fail, then I say to you, Gimli son of Glóin, that your hands shall flow with gold, and yet over you gold shall have no dominion.” - Lord of the Rings, Farewell to Lórien
Grasping means “greedy; avaricious; rapacious.” Avaricious means “immoderately desirous of wealth or gain; greedy.” Rapacious means “having or showing a strong or excessive desire to acquire money or possess things; greedy.”

Ungracious means “lacking social grace or graciousness; rude.” Rude means “insulting or uncivil; discourteous; impolite.” Discourteous means “showing bad manners; impolite; rude.”

Galadriel makes two comments on the general elvish perception of dwarves, telling us that they are seen as greedy and rude.

Now, let's talk about Galadriel and Gimli.

Many people say that Gimli does not feel romantic love for Galadriel; he just reveres her. Many others say that their relationship is an example of courtly love, and romantic love is an inherent part of courtly love.

There is no 'just' about Gimli's feelings, and they are far past reverence and admiration. His love for Galadriel is deep and eternal, greater than any other love he has or will ever feel. However, it is not romantic. He never says or does anything to imply romantic love (some symbolism that we traditionally think of as 'romantic' – like a lock of hair – is given. However, just because our culture has coded something as 'romantic', does not make it inherently so). He does not see her as his equal, but as someone far above him. He says it is enough just see and hear her; he does not have any desire to be with her romantically or sexually.

Gimli's comments are very odd comments for a dwarf. Dwarves see gems and gold as better than stars and nature:
They are a tough, thrawn race for the most part, secretive, laborious, retentive of the memory of injuries (and of benefits), lovers of stone, of gems, of things that take shape under the hands of the craftsmen rather than things that live by their own life. But they are not evil by nature, and few ever served the Enemy of free will, whatever the tales of Men alleged. - Lord of the Rings, Appendix F
Gimli has now said that Lórien is more beautiful than Moria, Galadriel is greater than any jewel, her hair is greater than all gold, and that the stars are greater than any gem. All of this is contrary to dwarven belief.

He will always cherish their first meeting, and honor and proclaim his love for her for the rest of his life.

As for Galadriel, she understands Gimli; reading his soul and perceiving his goodness. She understands that his request does not come from greed, but from love. So she fulfills it.
Gimli wept openly. 
“I have looked the last upon that which was fairest,” he said to Legolas his companion. “Henceforward I will call nothing fair, unless it be her gift.” He put his hand to his breast. 
“Tell me, Legolas, why did I come on this Quest? Little did I know where the chief peril lay! Truly Elrond spoke, saying that we could not foresee what we might meet upon our road. Torment in the dark was the danger that I feared, and it did not hold me back. But I would not have come, had I known the danger of light and joy. Now I have taken my worst wound in this parting, even if I were to go this night straight to the Dark Lord. Alas for Gimli son of Glóin!” 
“Nay!” said Legolas. “Alas for us all! And for all that walk the world in these after-days. For such is the way of it: to find and lose, as it seems to those whose boat is on the running stream. But I count you blessed, Gimli son of Glóin: for your loss you suffer of your own free will, and you might have chosen otherwise. But you have not forsaken your companions, and the least reward that you shall have is that the memory of Lothlórien shall remain ever clear and unstained in your heart, and shall neither fade nor grow stale.” 
“Maybe,” said Gimli; “and I thank you for your words. True words doubtless; yet all such comfort is cold. Memory is not what the heart desires. That is only a mirror, be it clear as Kheled-zâram. Or so says the heart of Gimli the Dwarf. Elves may see things otherwise. Indeed I have heard that for them memory is more like to the waking world than to a dream. Not so for Dwarves. 
But let us talk no more of it. Look to the boat! She is too low in the water with all this baggage, and the Great River is swift. I do not wish to drown my grief in cold water.” He took up a paddle, and steered towards the western bank, following Aragorn's boat ahead, which had already moved out of the middle stream. - Lord of the Rings, Farewell to Lórien
With Tolkien, “fair” is usually connected to inner beauty and goodness as well as outer beauty – remember that Frodo thought that Aragorn looked foul and felt fair when they met (see more on this here).

Gimli has been irrevocably changed by meeting Galadriel. He has finally felt that encompassing and indescribable awe of true love and joy, and now he has to let it go. Legolas says Gimli is blessed because he was selfless and chose to do what is right (keep his word and continue on the Quest), instead of what is easy. Thus, Gimli's memory will forever be spiritually unstained.

Legolas tries to comfort Gimli by focusing on the positive and morally good aspect of the situation. This is not as comforting to Gimli as Legolas intended it to be, though; because Gimli believes dwarven memory is different from elven memory (Gimli is only half right – elven memory is “more like to the waking world than to a dream,” but the elves view it as more of a burden than a gift; they desire more than just memory too).
[cut]; Gimli was fingering gold in his mind, and wondering if it were fit to be wrought into the housing of the Lady's gift. - Lord of the Rings, The Great River
Gimli is thinking of Galadriel's gift, and is not sure if gold is good enough for it.
“Praised be the bow of Galadriel, and the hand and eye of Legolas!” said Gimli, as he munched a wafer of lembas. “That was a mighty shot in the dark, my friend!” 
“But who can say what it hit?” said Legolas. 
“I cannot,” said Gimli. “But I am glad that the shadow came no nearer. I liked it not at all. Too much it reminded me of the shadow in Moria - the shadow of the Balrog,” he ended in a whisper. - Lord of the Rings, The Great River
Gimli praises Legolas's aim.
“Grievous is our loss,” said Legolas. “Yet we must needs make up our minds without his aid. Why cannot we decide, and so help Frodo? Let us call him back and then vote! I should vote for Minas Tirith.” 
“And so should I,” said Gimli. “We, of course, were only sent to help the Bearer along the road, to go no further than we wished; and none of us is under any oath or command to seek Mount Doom. Hard was my parting from Lothlórien. Yet I have come so far, and I say this: now we have reached the last choice, it is clear to me that I cannot leave Frodo. I would choose Minas Tirith, but if he does not, then I follow him.” 
“And I too will go with him,” said Legolas. “It would be faithless now to say farewell.” - Lord of the Rings, The Breaking of the Fellowship
Legolas and Gimli both agree that Minas Tirith is the best route, and that they will stay with Frodo. Gimli also mentions how hard it was for him to leave Lothlórien.
So it was that Legolas and Gimli found him. They came from the western slopes of the hill, silently, creeping through the trees as if they were hunting. Gimli had his axe in hand, and Legolas his long knife: all his arrows were spent. - Lord of the Rings, The Departure of Boromir
Legolas and Gimli both heard the horn of Gondor, and found each other on the way.
“Then let us do first what we must do,” said Legolas. “We have not the time or the tools to bury our comrade fitly, or to raise a mound over him. A cairn we might build.” 
“The labour would be hard and long: there are no stones that we could use nearer than the water-side,” said Gimli. - Lord of the Rings, The Departure of Boromir
Gimli rejects Legolas's plan with his knowledge of stone, but does not offer another solution.
“S is for Sauron,” said Gimli. “That is easy to read.” 
“Nay!” said Legolas. “Sauron does not use the Elf-runes.” 
“Neither does he use his right name, nor permit it to be spelt or spoken,” said Aragorn. - Lord of the Rings, The Departure of Boromir
While Legolas's bond with Gimli is certainly deep, they are not equals. Legolas and Aragorn are – they can talk about lore, or the unseen influences, because Aragorn was raised to understand Elvish thought (see more on Legolas and Aragorn here). This is the start of the pattern where Legolas corrects Gimli.
At the water-side Aragorn remained, watching the bier, while Legolas and Gimli hastened back on foot to Parth Galen. It was a mile or more, and it was some time before they came back, paddling two boats swiftly along the shore. - Lord of the Rings, The Departure of Boromir
Legolas and Gimli return for the boats.
“Here is another riddle!” said Gimli. “But it needs the light of day and for that we cannot wait.” 
“Yet however you read it, it seems not unhopeful,” said Legolas. - Lord of the Rings, The Riders of Rohan
Legolas insists that the dead orcs are a good sign.
“The brooch of an elven-cloak!” cried Legolas and Gimli together. - Lord of the Rings, The Riders of Rohan
Both Legolas and Gimli are surprised to see Pippin's brooch.
“Surely even Orcs must pause on the march?” said Gimli. 
“Seldom will Orcs journey in the open under the sun, yet these have done so,” said Legolas. “Certainly they will not rest by night.” 
“But if we walk by night, we cannot follow their trail,” said Gimli. 
“The trail is straight, and turns neither right nor left, as far as my eyes can see,” said Legolas. - Lord of the Rings, The Riders of Rohan
Legolas rejects both of Gimli's comments.
“Yet it would be rash to be sure of their counsels,” said Gimli. “And what of escape? In the dark we should have passed the signs that led you to the brooch.” 
“The Orcs will be doubly on their guard since then, and the prisoners even wearier,” said Legolas. “There will be no escape again, if we do not contrive it. How that is to be done cannot be guessed, but first we must overtake them.” 
“And yet even I, Dwarf of many journeys, and not the least hardy of my folk, cannot run all the way to Isengard without any pause,” said Gimli. “My heart burns me too, and I would have started sooner but now I must rest a little to run the better. And if we rest, then the blind night is the time to do so.” - Lord of the Rings, The Riders of Rohan
Legolas tells Gimli that the hobbits' escaping is impossible. Gimli is correct that now is the best time to rest.
“And tonight he is shrouded anyway,” Gimli murmured. “Would that the Lady had given us a light, such a gift as she gave to Frodo!” - Lord of the Rings, The Riders of Rohan
Gimli is thinking of Galadriel, and wishing that she had given them more gifts.
“But it is still dark,” said Gimli. “Even Legolas on a hill-top could not see them till the Sun is up.” 
“I fear they have passed beyond my sight from hill or plain, under moon or sun,” said Legolas. - Lord of the Rings, The Riders of Rohan
Gimli mentions Legolas's superior sight, and Legolas tells them that the orcs are too far away for him to see anything.
Often in their hearts they thanked the Lady of Lórien for the gift of lembas, for they could eat of it and find new strength even as they ran. - Lord of the Rings, The Riders of Rohan
Gimli is thinking of Galadriel, and thankful for her gift.
“Now do I most grudge a time of rest or any halt in our chase,” said Legolas. “The Orcs have run before us, as if the very whips of Sauron were behind them. I fear they have already reached the forest and the dark hills, and even now are passing into the shadows of the trees.” 
Gimli ground his teeth. “This is a bitter end to our hope and to all our toil!” he said. - Lord of the Rings, The Riders of Rohan
Legolas informs them of the orcs' movements.
“And ere morning it will be in the East,” said Legolas. “But rest if you must. Yet do not cast all hope away. Tomorrow is unknown. Rede oft is found at the rising of the Sun.” 
“Three suns already have risen on our chase and brought no counsel,” said Gimli. - Lord of the Rings, The Riders of Rohan
Legolas tries to give hope, but Gimli responds with negativity.
“Then Éomer son of Éomund, Third Marshal of Riddermark, let Gimli the Dwarf Glóin's son warn you against foolish words. You speak evil of that which is fair beyond the reach of your thought, and only little wit can excuse you.” 
“He stands not alone,” said Legolas, bending his bow and fitting an arrow with hands that moved quicker than sight. “You would die before your stroke fell.” - Lord of the Rings, The Riders of Rohan
Éomer infuriates Gimli with his comments about Galadriel. Gimli says that Éomer cannot comprehend how good and pure Galadriel is, and that stupidity can be his only excuse. Legolas is infuriated by Éomer's death threat, and immediately jumps to Gimli's defense (even though Gimli has been the antagonistic one).
“Come, you shall sit behind me, friend Gimli,” said Legolas. “Then all will be well, and you need neither borrow a horse nor be troubled by one.” 
Gimli was lifted up behind his friend, and he clung to him, not much more at ease than Sam Gamgee in a boat. - Lord of the Rings, The Riders of Rohan
Legolas calls Gimli a friend, and solves the problem by offering to have Gimli ride with him, reassuring Gimli that “all will be well.” Still greatly discomforted, Gimli clings to Legolas for support.
“And I will come, too,” said Gimli. “The matter of the Lady Galadriel lies still between us. I have yet to teach you gentle speech.” - Lord of the Rings, The Riders of Rohan
Gimli is not going to let Éomer's insults about Galadriel go. He will defend her to the death.
“We can do no more,” said Gimli sadly. “We have been set many riddles since we came to Tol Brandir, but this is the hardest to unravel. I would guess that the burned bones of the hobbits are now mingled with the Orcs'. It will be hard news for Frodo, if he lives to hear it; and hard too for the old hobbit who waits in Rivendell. Elrond was against their coming.” 
“But Gandalf was not,” said Legolas. 
“But Gandalf chose to come himself, and he was the first to be lost,” answered Gimli. “His foresight failed him.” 
“The counsel of Gandalf was not founded on foreknowledge of safety, for himself or for others,” said Aragorn. “There are some things that it is better to begin than to refuse, even though the end may be dark.” - Lord of the Rings, The Riders of Rohan
Gimli believes that Merry and Pippin are dead, and that Gandalf was wrong. He believes that Gandalf's wisdom failed because Gandalf died. Legolas and Aragorn disagree with him, because they see the higher purpose of Gandalf's wisdom.
“Only a few hours ago you were unwilling to sit on a horse of Rohan,” laughed Legolas. “You will make a rider yet.” 
“It seems unlikely that I shall have the chance,” said Gimli. - Lord of the Rings, The Riders of Rohan
Gimli's dismay at the loss of the horses amuses Legolas, causing him to make a joke about Gimli's change of heart.
“And do not forget that old man!” said Gimli. “I should be happier if I could see the print of a boot.” 
“Why would that make you happy?” said Legolas. 
“Because an old man with feet that leave marks might be no more than he seemed,” answered the Dwarf. 
“Maybe,” said the Elf; “but a heavy boot might leave no print here: the grass is deep and springy.” 
“That would not baffle a Ranger,” said Gimli. “A bent blade is enough for Aragorn to read. But I do not expect him to find any traces. It was an evil phantom of Saruman that we saw last night. I am sure of it, even under the light of morning. His eyes are looking out on us from Fangorn even now, maybe.” 
“It is likely enough,” said Aragorn; “yet I am not sure. I am thinking of the horses. You said last night, Gimli, that they were scared away. But I did not think so. Did you hear them, Legolas? Did they sound to you like beasts in terror?” 
“No,” said Legolas. “I heard them clearly. But for the darkness and our own fear I should have guessed that they were beasts wild with some sudden gladness. They spoke as horses will when they meet a friend that they have long missed.” 
“So I thought,” said Aragorn; “but I cannot read the riddle, unless they return.” - Lord of the Rings, The White Rider
Legolas is skeptical about Gimli's comments about boots, and both Legolas and Aragorn disagree with Gimli about why the horses ran away.
“There was sorcery here right enough,” said Gimli. “What was that old man doing? What have you to say, Aragorn, to the reading of Legolas. Can you better it?” - Lord of the Rings, The White Rider
Gimli agrees with Legolas's assessment, and wonders if Aragorn can add anything to it.
“Then we must go in, too,” said Gimli. “But I do not like the look of this Fangorn: and we were warned against it. I wish the chase had led anywhere else!” 
“I do not think the wood feels evil, whatever tales may say,” said Legolas. He stood under the eaves of the forest, stooping forward, as if he were listening, and peering with wide eyes into the shadows. “No, it is not evil; or what evil is in it is far away. I catch only the faintest echoes of dark places where the hearts of the trees are black. There is no malice near us; but there is watchfulness, and anger.” 
“Well, it has no cause to be angry with me,” said Gimli. “I have done it no harm.” 
“That is just as well,” said Legolas. “But nonetheless it has suffered harm. There is something happening inside, or going to happen. Do you not feel the tenseness? It takes my breath.” 
“I feel the air is stuffy,” said the Dwarf. “This wood is lighter than Mirkwood, but it is musty and shabby.” 
“It is old, very old,” said the Elf. “So old that almost I feel young again, as I have not felt since I journeyed with you children. It is old and full of memory. I could have been happy here, if I had come in days of peace.” 
“I dare say you could,” snorted Gimli. “You are a Wood-elf, anyway, though Elves of any kind are strange folk. Yet you comfort me. Where you go, I will go. But keep your bow ready to hand, and I will keep my axe loose in my belt. Not for use on trees,” he added hastily, looking up at the tree under which they stood. “I do not wish to meet that old man at unawares without an argument ready to hand, that is all. Let us go!” - Lord of the Rings, The White Rider
Legolas explains Fangorn to Gimli, and Gimli responds that elves are odd. Fangorn makes Gimli feel uncomfortable, but Legolas's presence comforts and reassures him, giving him strength.
“But we did not wish to come to Fangorn,” said Gimli. 
“Yet here we are-and nicely caught in the net,” said Legolas. “Look!” 
“Look at what?” said Gimli. 
“There in the trees.” 
“Where? I have not elf-eyes.” 
“Hush! Speak more softly! Look!” said Legolas pointing. “Down in the wood, back in the Way that we have just come. It is he. Cannot you see him, passing from tree to tree?” 
“I see, I see now!” hissed Gimli. - Lord of the Rings, The White Rider
Legolas tells Gimli where to look and how to speak, and asks if he can see the figure.
Gimli gazed with wide eyes for a while, as step by step the figure drew nearer. Then suddenly, unable to contain himself longer, he burst out: “Your bow, Legolas! Bend it! Get ready! It is Saruman. Do not let him speak, or put a spell upon us! Shoot first!” 
Legolas took his bow and bent it, slowly and as if some other will resisted him. He held an arrow loosely in his hand but did not fit it to the string. Aragorn stood silent, his face was watchful and intent. 
“Why are you waiting? What is the matter with you?” said Gimli in a hissing whisper. 
“Legolas is right,” said Aragorn quietly. “We may not shoot an old man so, at unawares and unchallenged, whatever fear or doubt be on us. Watch and wait!” - Lord of the Rings, The White Rider
Gimli tells Legolas to shoot, and does not understand why he doesn't. To Gimli, the matter is clear: the figure is Saruman, and they need to strike first. Something must be mentally wrong with Legolas, for him to hesitate.

Aragorn responds to Gimli's criticism, telling him that Legolas is right and that it would be amoral for them to act that way.
At last the old man broke the silence. “Well met indeed, my friends,” he said in a soft voice. “I wish to speak to you. Will you come down or shall I come up?” Without waiting for an answer he began to climb. 
“Now!” said Gimli. “Stop him, Legolas!” 
“Did I not say that I wished to speak to you?” said the old man. “Put away that bow, Master Elf!” - Lord of the Rings, The White Rider
Gimli once again tells Legolas to shoot, even though the “old man” is behaving peacefully.
“Then she sent me no message?” said Gimli and bent his head. 
“Dark are her words,” said Legolas, “and little do they mean to those that receive them.” 
“That is no comfort,” said Gimli. 
“What then?” said Legolas. “Would you have her speak openly to you of your death?” 
“Yes, if she had nought else to say.” 
“What is that?” said Gandalf, opening his eyes. “Yes, I think I can guess what her words may mean. Your pardon, Gimli! I was pondering the messages once again. But indeed she sent words to you, and neither dark nor sad. 
'To Gimli son of Glóin,” she said, “give his Lady's greeting. Lock-bearer, wherever thou goest my thought goes with thee. But have a care to lay thine axe to the right tree!'” 
“In happy hour you have returned to us, Gandalf,” cried the Dwarf, capering as he sang loudly in the strange dwarf-tongue. “Come, come!” he shouted, swinging his axe. “Since Gandalf's head is now sacred, let us find one that it is right to cleave!” - Lord of the Rings, The White Rider
Gimli would rather have a message of death from Galadriel, than no message at all. This shows again just how great his love for her is.

Galadriel uses the word thee, which is a form of affection:

Appendix F, II On Translation says,
In one or two places an attempt has been made to hint at these distinctions by an inconsistent use of thou. Since this pronoun is now unusual and archaic it is employed mainly to represent the use of ceremonious language; but a change from you to thou, thee is sometimes meant to show, there being no other means of doing this, a significant change from the deferential, or between men and women normal, forms to the familiar.
And HME 12 says,
Where thou, thee, thy, appears it is used mainly to mark a use of the familiar form where that was no usual. For instance its use by Denethor in his last madness to Gandalf, and by the Messenger of Sauron, was in both cases intended to be contemptuous. But elsewhere it is occasionally used to indicate a deliberate change to a form of affection or endearment.
(For more on this, see this essay)

Galadriel knows she has Gimli's love and refers to herself as his Lady, she gives him an affectionate greeting, and tells him that he is in her thoughts. Galadriel does not see him as her equal or feel any romantic love for him – she is happily married to Celeborn – but she does feel “love and understanding” for him. She saw from the beginning that Gimli is a good soul.

Gimli is ecstatic at having a message from Galadriel.
“Then it is true, as Éomer reported, that you are in league with the Sorceress of the Golden Wood?” said Wormtongue. “It is not to be wondered at: webs of deceit were ever woven in Dwimordene.” 
Gimli strode a pace forward, but felt suddenly the hand of Gandalf clutch him by the shoulder, and he halted, standing stiff as stone. - Lord of the Rings, The King of the Golden Hall
Gandalf has to stop Gimli from attacking Wormtongue. Gimli obeys, but his fury is still clear.
Gimli walked with Legolas, his axe on his shoulder. “Well, at last we set off!” he said. “Men need many words before deeds. My axe is restless in my hands. Though I doubt not that these Rohirrim are fell-handed when they come to it. Nonetheless this is not the warfare that suits me. How shall I come to the battle? I wish I could walk and not bump like a sack at Gandalf's saddlebow.” 
“A safer seat than many, I guess,” said Legolas. “Yet doubtless Gandalf will gladly put you down on your feet when blows begin; or Shadowfax himself. An axe is no weapon for a rider.” 
“And a Dwarf is no horseman. It is orc-necks I would hew, not shave the scalps of Men,” said Gimli, patting the haft of his axe. - Lord of the Rings, The King of the Golden Hall
Legolas and Gimli agree that Gimli is not suited for fighting on horseback.
“I will forget my wrath for a while, Éomer son of Éomund,” said Gimli; “but if ever you chance to see the Lady Galadriel with your eyes, then you shall acknowledge her the fairest of ladies, or our friendship will end.” - Lord of the Rings, The King of the Golden Hall
Remember, fair is usually connected to inner beauty and goodness as well as outer beauty. Wrath means “a feeling of intense anger.”

Gimli warns Éomer that he will let go of his fury for now, but that if Éomer ever meets Galadriel, then Éomer must acknowledge that she is the most beautiful and noble lady alive.
“I thank you indeed,” said Gimli greatly pleased. “I will gladly go with you, if Legolas, my comrade, may ride beside us.” - Lord of the Rings, The King of the Golden Hall
Comrade means “a person who shares in one's activities, occupation, etc.; companion, associate, or friend.”

Gimli tells Éomer they will ride together only if Legolas can accompany them.
Gimli stood leaning against the breastwork upon the wall. Legolas sat above on the parapet, fingering his bow, and peering out into the gloom. 
“This is more to my liking,” said the dwarf, stamping on the stones. “Ever my heart rises as we draw near the mountains. There is good rock here. This country has tough bones. I felt them in my feet as we came up from the dike. Give me a year and a hundred of my kin and I would make this a place that armies would break upon like water.” 
“I do not doubt it,” said Legolas. “But you are a dwarf, and dwarves are strange folk. I do not like this place, and I shall like it no more by the light of day. But you comfort me, Gimli, and I am glad to have you standing nigh with your stout legs and your hard axe. I wish there were more of your kin among us. But even more would I give for a hundred good archers of Mirkwood. We shall need them. The Rohirrim have good bowmen after their fashion, but there are too few here, too few. 
“It is dark for archery,” said Gimli. “Indeed it is time for sleep. Sleep! I feel the need of it, as never I thought any dwarf could. Riding is tiring work. Yet my axe is restless in my hand. Give me a row of orc-necks and room to swing and all weariness will fall from me!” - Lord of the Rings, Helm's Deep
Paralleling the earlier scene, it is now Legolas's turn to say that dwarves are odd, and that stone makes him feel uncomfortable; but that Gimli's presence comforts and reassures him, giving him strength. He goes on to say that he would like more of his own kin there than Gimli's, simply because they are better archers.
“Two!” said Gimli, patting his axe. He had returned to his place on the wall. 
“Two?” said Legolas. “I have done better, though now I must grope for spent arrows; all mine are gone. Yet I make my tale twenty at the least. But that is only a few leaves in a forest.” - Lord of the Rings, Helm's Deep
Legolas and Gimli do not fight together, but they compete to see who can kill more enemies.
Down from the wall leapt Gimli with a fierce cry that echoed in the cliffs. “Khazâd! Khazâd!” He soon had work enough. 
“Ai-oi!” he shouted. “The Orcs are behind the wall. Ai-oi! Come, Legolas! There are enough for us both. Khazâd ai-mênu! 
“Twenty-one!” cried Gimli. He hewed a two-handed stroke and laid the last Orc before his feet. “Now my count passes Master Legolas again.” 
He climbed up and found Legolas beside Aragorn and Éomer. The elf was whetting his long knife. There was for a while a lull in the assault, since the attempt to break in through the culvert had been foiled. 
“Twenty-one!” said Gimli. 
“Good!” said Legolas. “But my count is now two dozen. It has been knife-work up here.” - Lord of the Rings, Helm's Deep
Gimli calls for Legolas to come, as he attacks the enemy. Legolas doesn't, choosing to stay with Aragorn.

Gimli is excited to pass Legolas's previous score, but he then finds out that Legolas is still winning the game.
Legolas: “Where is Gimli?” 
“I do not know.” said Aragorn. “I last saw him fighting on the ground behind the wall, but the enemy swept us apart.” 
“Alas! That is evil news,” said Legolas. 
“He is stout and strong,” said Aragorn. “Let us hope that he will escape back to the caves. There he would be safe for a while. Safer than we. Such a refuge would be to the liking of a dwarf.” 
“That must be my hope,” said Legolas. “But I wish that he had come this way. I desired to tell Master Gimli that my tale is now thirty-nine.” 
“If he wins back to the caves, he will pass your count again,” laughed Aragorn. “Never did I see an axe so wielded.” - Lord of the Rings, Helm's Deep
Legolas worries about Gimli, and says that he wanted to tell Gimli his updated score.
“Forty-two, Master Legolas!” he cried. “Alas! My axe is notched: the forty-second had an iron collar on his neck. How is it with you?” 
“You have passed my score by one,” answered Legolas. “But I do not grudge you the game, so glad am I to see you on your legs!” - Lord of the Rings, The Road to Isengard
Legolas tells Gimli he doesn't mind losing their competition because he is so happy to see that Gimli is still alive.
Legolas and Gimli were now riding together upon one horse; and they kept close beside Gandalf, for Gimli was afraid of the wood. 
They rode in silence for a while; but Legolas was ever glancing from side to side, and would often have halted to listen to the sounds of the wood, if Gimli had allowed it. 
“These are the strangest trees that ever I saw,” he said; “and I have seen many an oak grow from acorn to ruinous age. I wish that there were leisure now to walk among them: they have voices, and in time I might come to understand their thought.” 
“No, no!” said Gimli. “Let us leave them! I guess their thought already: hatred of all that go on two legs; and their speech is of crushing and strangling.” 
“Not of all that go on two legs,” said Legolas. “There I think you are wrong. It is Orcs that they hate. For they do not belong here and know little of Elves and Men. Far away are the valleys where they sprang. From the deep dales of Fangorn, Gimli, that is whence they come, I guess.” 
“Then that is the most perilous wood in Middle-earth,” said Gimli. “I should be grateful for the part they have played, but I do not love them. You may think them wonderful, but I have seen a greater wonder in this land, more beautiful than any grove or glade that ever grew: my heart is still full of ft. Strange are the ways of Men, Legolas! Here they have one of the marvels of the Northern World, and what do they say of it? Caves, they say! Caves! Holes to fly to in time of war, to store fodder in! My good Legolas, do you know that the caverns of Helm's Deep are vast and beautiful? There would be an endless pilgrimage of Dwarves, merely to gaze at them, if such things were known to be. Aye indeed, they would pay pure gold for a brief glance!” 
“And I would give gold to be excused,” said Legolas; “and double to be let out, if I strayed in!” 
“You have not seen, so I forgive your jest,” said Gimli. “But you speak like a fool. Do you think those halls are fair, where your King dwells under the hill in Mirkwood, and Dwarves helped in their making long ago? They are but hovels compared with the caverns I have seen here: immeasurable halls, filled with an everlasting music of water that tinkles into pools, as fair as Kheled-zâram in the starlight. And, Legolas, when the torches are kindled and men walk on the sandy floors under the echoing domes, ah! then, Legolas, gems and crystals and veins of precious ore glint in the polished walls; and the light glows through folded marbles, shell-like, translucent as the living hands of Queen Galadriel. There are columns of white and saffron and dawn-rose, Legolas, fluted and twisted into dreamlike forms; they spring up from many-coloured floors to meet the glistening pendants of the roof: wings, ropes, curtains fine as frozen clouds; spears, banners, pinnacles of suspended palaces! Still lakes mirror them: a glimmering world looks up from dark pools covered with clear glass; cities. such as the mind of Durin could scarce have imagined in his sleep, stretch on through avenues and pillared courts, on into the dark recesses where no light can come. And plink! a silver drop falls, and the round wrinkles in the glass make all the towers bend and waver like weeds and corals in a grotto of the sea. Then evening comes: they fade and twinkle out; the torches pass on into another chamber and another dream. There is chamber after chamber, Legolas; hall opening out of hall, dome after dome, stair beyond stair; and still the winding paths lead on into the mountains' heart. Caves! The Caverns of Helm's Deep! Happy was the chance that drove me there! It makes me weep to leave them.” 
“Then I will wish you this fortune for your comfort, Gimli,” said the Elf, “that you may come safe from war and return to see them again. But do not tell all your kindred! There seems little left for them to do, from your account. Maybe the men of this land are wise to say little: one family of busy dwarves with hammer and chisel might mar more than they made.” 
“No, you do not understand,” said Gimli. “No dwarf could be unmoved by such loveliness. None of Durin's race would mine those caves for stones or ore, not if diamonds and gold could be got there. Do you cut down groves of blossoming trees in the spring-time for firewood? We would tend these glades of flowering stone, not quarry them. With cautious skill, tap by tap - a small chip of rock and no more, perhaps, in a whole anxious day - so we could work, and as the years went by, we should open up new ways, and display far chambers that are still dark, glimpsed only as a void beyond fissures in the rock. And lights, Legolas! We should make lights, such lamps as once shone in Khazad-dûm; and when we wished we would drive away the night that has lain there since the hills were made; and when we desired rest, we would let the night return.” 
“You move me, Gimli,” said Legolas. “I have never heard you speak like this before. Almost you make me regret that I have not seen these caves. Come! Let us make this bargain – if we both return safe out of the perils that await us, we will journey for a while together. You shall visit Fangorn with me, and then I will come with you to see Helm's Deep. 
“That would not be the way of return that I should choose,” said Gimli. “But I will endure Fangorn, if I have your promise to come back to the caves and share their wonder with me.” 
“You have my promise,” said Legolas. “But alas! Now we must leave behind both cave and wood for a while: See! We are coming to the end of the trees.” - Lord of the Rings, The Road to Isengard
Legolas has the insight into the wood, while Gimli is afraid of it. Gimli then starts to eagerly tell Legolas about the Glittering Caves.

Even though he is now good friends with Gimli, Legolas still holds some prejudice against dwarves. Gimli is clearly ecstatic and eagerly sharing with Legolas the wonder of the Glittering Caves, and Legolas responds with a joke that insults them. Gimli is right to call him out and remind him of the role the dwarves played in building his own home.

Gimli then continues describing the beauty of the Glittering Caves, and draws a parallel between them and the hands of “Queen Galadriel.” Even though Galadriel is not a queen, Gimli calling her so shows how he sees and honors her as such a high and noble being.

Legolas starts to understand, but it is clear he doesn't fully understand. He tells Gimli that he hopes Gimli can return someday, but then warns Gimli not to tell other dwarves, because they may harm the Glittering Caves. This is another sign of Legolas's lingering prejudice against dwarves.

Gimli doesn't get offended, but instead tells Legolas that he misunderstands. Gimli then tries to use metaphors Legolas will understand. Legolas finally does understand, and is moved. This prompts him to make an equal bargain – he will open himself up to sharing in the beauty of the Glittering Caves with Gimli, if Gimli will agree to open himself up to the wonder of Fangorn.
The others, surprised by his cry, halted and turned; but Legolas started to ride back. 
“No, no!” cried Gimli. “Do as you please in your madness, but let me first get down from this horse! I wish to see no eyes!” - Lord of the Rings, The Road to Isengard
Gimli believes Legolas is insane, and wants nothing to do with any eyes, thank you very much!
“And what about your companions? What about Legolas and me?” cried Gimli, unable to contain himself longer. “You rascals, you woolly-footed and wool-pated truants! A fine hunt you have led us! Two hundred leagues, through fen and forest, battle and death, to rescue you! And here we find you feasting and idling-and smoking! Smoking! Where did you come by the weed, you villains? Hammer and tongs! I am so torn between rage and joy, that if I do not burst, it will be a marvel!” 
“You speak for me, Gimli,” laughed Legolas. “Though I would sooner learn how they came by the wine.” - Lord of the Rings, The Road to Isengard
Legolas finds Gimli's rant funny, and says he would rather have wine than pipe-weed.
“You have drunk of the waters of the Ents, have you?” said Legolas. “Ah, then I think it is likely that Gimli's eyes do not deceive him. Strange songs have been sung of the draughts of Fangorn.” - Lord of the Rings, Flotsam and Jetsam
Legolas has heard things about “the draughts of Fangorn.”
“Nay!” said Gimli. “Legolas and I wish for a closer view. We alone here represent our kindred. We also will come behind.” - Lord of the Rings, The Voice of Saruman
Gimli speaks up for both himself and Legolas.
Legolas: “I should dearly love to journey in Fangorn's Wood. I scarcely passed beyond the eaves of it, and I did not wish to turn back.” 
Treebeard's eyes gleamed with pleasure. “I hope you may have your wish, ere the hills be much older,” he said. 
“I will come, if I have the fortune,” said Legolas. “I have made a bargain with my friend that, if all goes well, we will visit Fangorn together - by your leave.” 
“Any Elf that comes with you will be welcome,” said Treebeard. 
“The friend I speak of is not an Elf,” said Legolas; “I mean Gimli, Glóin's son here.” Gimli bowed low, and the axe slipped from his belt and clattered on the ground. 
“Hoom, hm! Ah now,” said Treebeard, looking dark-eyed at him. “A dwarf and an axe-bearer! Hoom! I have good will to Elves; but you ask much. This is a strange friendship!” 
“Strange it may seem,” said Legolas; “but while Gimli lives I shall not come to Fangorn alone. His axe is not for trees, but for orc-necks, O Fangorn, Master of Fangorn's Wood. Forty-two he hewed in the battle.” 
“Hoo! Come now!” said Treebeard. “That is a better story! Well, well, things will go as they will; and there is no need to hurry to meet them. But now we must part for a while.” - Lord of the Rings, The Voice of Saruman
To truly understand this scene, we have to know the history of the ents.
Now when Aulë laboured in the making of the Dwarves he kept this work hidden from the other Valar; but at last he opened his mind to Yavanna and told her of all that had come to pass. Then Yavanna said to him: “Eru is merciful. Now I see that thy heart rejoiceth, as indeed it may; for thou hast received not only forgiveness but bounty. Yet because thou hiddest this thought from me until its achievement, thy children will have little love for the things of my love. They will love first the things made by their own hands, as doth their father. They will delve in the earth, and the things that grow and live upon the earth they will not heed. Many a tree shall feel the bite of their iron without pity. 
But Aulë answered: “That shall also be true of the Children of Ilúvatar; for they will eat and they will build. And though the things of thy realm have worth in themselves, and would have worth if no Children were to come, yet Eru will give them dominion, and they shall use all that they find in Arda: though not, by the purpose of Eru, without respect or without gratitude.” 
“Not unless Melkor darken their hearts,” said Yavanna. And she was not appeased, but grieved in heart, fearing what might be done upon Middle-earth in days to come. Therefore she went before Manwë, and she did not betray the counsel of Aulë, but she said: “King of Arda, is it true, as Aulë hath said to me, that the Children when they come shall have dominion over all the things of my labour, to do as they will therewith?” 
“Nay,” he said, “only the trees of Aulë will be tall enough. In the mountains the Eagles shall house, and hear the voices of those who call upon us. But in the forests shall walk the Shepherds of the Trees.” 
Then Manwë and Yavanna parted for that time, and Yavanna returned to Aulë; and he was in his smithy, pouring molten metal into a mould. “Eru is bountiful,” she said. “Now let thy children beware! For there shall walk a power in the forests whose wrath they will arouse at their peril.” - The Silmarillion, Of Aulë and Yavanna
The ents were originally created to offset the creation of the dwarves. Legolas likely knows this, as he has heard many songs and tales about the ents. Treebeard automatically assumes the friend Legolas is talking about if an elf, and grants permission because the ents like the elves. When he learns Legolas means Gimli, he calls their friendship strange and says Legolas asks a lot from him. Treebeard's prejudice is clear. However, neither Legolas nor Gimli get upset, and Legolas is both open-minded and assertive in his defense of Gimli and their friendship. He has made a promise and he won't break it; even if that means giving up his much-wanted chance to explore Fangorn.
Aragorn: “But for myself, and any that will go with me . . .” 
“I for one!” cried Legolas. 
“And Gimli with him!” said the Dwarf. 
Soon all were ready to depart: twenty-four horses, with Gimli behind Legolas, and Merry in front of Aragorn. - Lord of the Rings, The Passing of the Grey Company
Legolas and Gimli ride together again, and both insist they will stay with Aragorn.
Merry slept until he was roused by Legolas and Gimli. “The Sun is high,” said Legolas. “All others are up and doing. Come, Master Sluggard, and look at this place while you may!” 
“There was a battle here three nights ago,” said Gimli, “and here Legolas and I played a game that I won only by a single orc. Come and see how it was! And there are caves, Merry, caves of wonder! Shall we visit them, Legolas, do you think? 
Nay! There is no time,” said the Elf. “Do not spoil the wonder with haste! I have given you my word to return hither with you, if a day of peace and freedom comes again. But it is now near to noon, and at that hour we eat, and then set out again, I hear.” - Lord of the Rings, The Passing of the Grey Company
Gimli asks Legolas for his opinion, and Legolas has the wisdom to know that waiting is best.
“They are a strange company, these newcomers,” said Gimli. “Stout men and lordly they are, and the Riders of Rohan look almost as boys beside them; for they are grim men of face, worn like weathered rocks for the most part, even as Aragorn himself; and they are silent.” 
“But even as Aragorn they are courteous, if they break their silence,” said Legolas. “And have you marked the brethren Elladan and Elrohir? Less sombre is their gear than the others’, and they are fair and gallant as Elven-lords; and that is not to be wondered at in the sons of Elrond of Rivendell.” - Lord of the Rings, The Passing of the Grey Company
Legolas counters Gimli's statements on the Grey Company. He also speaks highly of Elladan and Elrohir, but from an impersonal standpoint – 'Elrond is a famous elven lord, so it is not surprising that his sons are good and brave'.
Gimli: “Gandalf sent it, I would guess.” 
“Nay, Galadriel,” said Legolas. “Did she not speak through Gandalf of the ride of the Grey Company from the North?” 
“Yes, you have it,” said Gimli. “The Lady of the Wood! She read many hearts and desires. Now why did not we wish for some of our own kinsfolk, Legolas?” 
Legolas stood before the gate and turned his bright eyes away north and east, and his fair face was troubled. “I do not think that any would come,” he answered. “They have no need to ride to war; war already marches on their own lands.” 
For a while the three companions walked together, speaking of this and that turn of the battle, and they went down from the broken gate, and passed the mounds of the fallen on the greensward beside the road, until they stood on Helm’s Dike and looked into the Coomb. - Lord of the Rings, The Passing of the Grey Company
Legolas once again has the wisdom and insight into the situation.
Behind them walked Legolas and Gimli. 
His knees shook, and he was wroth with himself. “Here is a thing unheard of!” he said. “An Elf will go underground and a Dwarf dare not!” With that he plunged in. 
The Company now mounted again, and Gimli returned to Legolas. 
Legolas turning to speak to Gimli looked back and the Dwarf saw before his face the glitter in the Elf’s bright eyes. - Lord of the Rings, The Passing of the Grey Company
Legolas and Gimli went looking for Aragorn, and then once again ride together. There is a hint of competitiveness in Gimli's anger at himself for fearing the Paths of the Dead when Legolas doesn't.
Legolas and Gimli were early abroad, and they begged leave to go up into the City; for they were eager to see Merry and Pippin. 
“It is good to learn that they are still alive,” said Gimli; “for they cost us great pains in our march over Rohan, and I would not have such pains all wasted.” 
Together the Elf and the Dwarf entered Minas Tirith, and folk that saw them pass marvelled to see such companions; for Legolas was fair of face beyond the measure of Men, and he sang an elven-song in a clear voice as he walked in the morning; but Gimli stalked beside him, stroking his beard and staring about him. 
“There is some good stone-work here,” he said as he looked at the walls; “but also some that is less good, and the streets could be better contrived. When Aragorn comes into his own, I shall offer him the service of stonewrights of the Mountain, and we will make this a town to be proud of.” 
“They need more gardens,” said Legolas. “The houses are dead, and there is too little here that grows and is glad. If Aragorn comes into his own, the people of the Wood shall bring him birds that sing and trees that do not die.” - Lord of the Rings, The Last Debate
Some people believe that Gimli has more faith in Aragorn because he says “when” and Legolas says “if”. However, that is not true (see my Legolas and Aragorn essay, link above). Legolas has the wisdom to know that victory is still far from a sure thing.

Both Legolas and Gimli plan to use the strengths of their races to help Aragorn, thus creating a city that has elements of all three cultures.
“I am one of the Nine Companions who set out with Mithrandir from Imladris,” said Legolas; “and with this Dwarf, my friend, I came with the Lord Aragorn. But now we wish to see our friends, Meriadoc and Peregrin, who are in your keeping, we are told.” 
“That is a fair lord and a great captain of men,” said Legolas. “If Gondor has such men still in these days of fading, great must have been its glory in the days of its rising.” 
“And doubtless the good stone-work is the older and was wrought in the first building,” said Gimli. “It is ever so with the things that Men begin: there is a frost in Spring, or a blight in Summer, and they fail of their promise.” 
“Yet seldom do they fail of their seed,” said Legolas. “And that will lie in the dust and rot to spring up again in times and places unlooked-for. The deeds of Men will outlast us, Gimli.” 
“And yet come to naught in the end but might-have-beens, I guess,” said the Dwarf. 
“To that the Elves know not the answer,” said Legolas. - Lord of the Rings, The Last Debate
Gimli makes some prejudiced comments about humans. Legolas recognizes Imrahil's goodness and once again has the insight on the subject matter.
Legolas: “Alas! for the gulls. No peace shall I have again under beech or under elm.” 
“Say not so!” said Gimli. “There are countless things still to see in Middle-earth, and great works to do. But if all the fair folk take to the Havens, it will be a duller world for those who are doomed to stay.” - Lord of the Rings, The Last Debate
Gimli likes the elves, and cares greatly about Legolas; he does not want them to leave.
“Not willingly,” said Gimli. “For upon that road I was put to shame: Gimli Glóin’s son, who had deemed himself more tough than Men, and hardier under earth than any Elf. But neither did I prove; and I was held to the road only by the will of Aragorn.” 
And by the love of him also,” said Legolas. “For all those who come to know him come to love him after his own fashion, even the cold maiden of the Rohirrim. It was at early morn of the day ere you came there, Merry, that we left Dunharrow, and such a fear was on all the folk that none would look on our going, save the Lady Éowyn, who lies now hurt in the House below. There was grief at that parting, and I was grieved to behold it.” 
“Alas! I had heart only for myself,” said Gimli. “Nay! I will not speak of that journey.” - Lord of the Rings, The Last Debate
Gimli says he was the weakest member of the group during the Paths of the Dead.
Gimli: “Ere that dark day ended none of the enemy were left to resist us all were drowned, or were flying south in the hope to find their own lands upon foot. Strange and wonderful I thought it that the designs of Mordor should be overthrown by such wraiths of fear and darkness. With its own weapons was it worsted!” 
“Strange indeed,” said Legolas. “In that hour I looked on Aragorn and thought how great and terrible a Lord he might have become in the strength of his will, had he taken the Ring to himself. Not for naught does Mordor fear him. But nobler is his spirit than the understanding of Sauron; for is he not of the children of Lúthien? Never shall that line fail, though the years may lengthen beyond count.” 
“Beyond the eyes of the Dwarves are such foretellings,” said Gimli. “But mighty indeed was Aragorn that day.” - Lord of the Rings, The Last Debate
Legolas and Gimli agree it was strange that darkness worked against darkness. Legolas then has the insight into the line of Lúthien.
Gimli: “Heavy would my heart have been, for all our victory at the havens, if Legolas had not laughed suddenly. 
“Up with your beard, Durin’s son!” he said. “For thus is it spoken: Oft hope is born, when all is forlorn.” But what hope he saw from afar he would not tell. When night came it did but deepen the darkness, and our hearts were hot, for away in the North we saw a red glow under the cloud, and Aragorn said: “Minas Tirith is burning.” 
But at midnight hope was indeed born anew. Sea-crafty men of the Ethir gazing southward spoke of a change coming with a fresh wind from the Sea. Long ere day the masted ships hoisted sail; and our speed grew, until dawn whitened the foam at our prows. And so it was, as you know, that we came in the third hour of the morning with a fair wind and the Sun unveiled, and we unfurled the great standard in battle. It was a great day and a great hour, whatever may come after.” 
“Follow what may, great deeds are not lessened in worth,” said Legolas. “Great deed was the riding of the Paths of the Dead, and great it shall remain, though none be left in Gondor to sing of it in the days that are to come.” 
“And that may well befall,” said Gimli. “For the faces of Aragorn and Gandalf are grave. Much I wonder what counsels they are taking in the tents there below. For my part, like Merry, I wish that with our victory the war was now over. Yet whatever is still to do, I hope to have a part in it, for the honour of the folk of the Lonely Mountain.” 
“And I for the folk of the Great Wood,” said Legolas, “and for the love of the Lord of the White Tree.” - Lord of the Rings, The Last Debate
Legolas has a moment of foresight, and sees that a Greater Power will help them. He then continues Gimli's statement with a piece of wisdom. Both Legolas and Gimli want to be involved in whatever comes next, to bring honor to their people. Legolas also wants to do so out of love for Aragorn (see my Legolas and Aragorn essay, link above).
Legolas and Gimli were to ride again together in the company of Aragorn and Gandalf, who went in the van with the Dúnedain and the sons of Elrond. 
There was Gandalf as chief herald, and Aragorn with the sons of Elrond, and Éomer of Rohan, and Imrahil; and Legolas and Gimli and Peregrin were bidden to go also, so that all the enemies of Mordor should have a witness. - Lord of the Rings, The Black Gate Opens
Legolas and Gimli once again ride together, and they go with the others to speak to the Mouth of Sauron.
And when they were arrayed they went to the great feast; and they sat at the King’s table with Gandalf, and King Éomer of Rohan, and the Prince Imrahil and all the chief captains; and there also were Gimli and Legolas. 
[cut]; and they talked deep into the night with Merry and Pippin and Gandalf, and after a while Legolas and Gimli joined them. - Lord of the Rings, The Field of Cormallen
They both catch up with Frodo and Sam.
And before he went to his rest he sent for Gimli the Dwarf, and he said to him: “Gimli Glóin’s son, have you your axe ready?” 
“Nay, lord,” said Gimli, “but I can speedily fetch it, if there be need.” 
“You shall judge,” said Éomer. “For there are certain rash words concerning the Lady in the Golden Wood that lie still between us. And now I have seen her with my eyes.” 
“Well, lord,” said Gimli, “and what say you now?” 
“Alas!” said Éomer. “I will not say that she is the fairest lady that lives.” 
“Then I must go for my axe,” said Gimli. 
“But first I will plead this excuse,” said Éomer. “Had I seen her in other company, I would have said all that you could wish. But now I will put Queen Arwen Evenstar first, and I am ready to do battle on my own part with any who deny me. Shall I call for my sword?” 
Then Gimli bowed low. “Nay, you are excused for my part, lord,” he said. “You have chosen the Evening; but my love is given to the Morning. And my heart forebodes that soon it will past away for ever.” - Lord of the Rings, Many Partings
Gimli understands Éomer's choice, and his response is melancholic. He loves Galadriel, and he knows that soon she will be gone from Middle-earth forever.
For the other Companions steeds were furnished according to their stature; and Frodo and Samwise rode at Aragorn’s side, and Gandalf rode upon Shadowfax, and Pippin rode with the knights of Gondor; and Legolas and Gimli as ever rode together upon Arod. - Lord of the Rings, Many Partings
As ever means “typical, traditional, and usual.” Gimli has almost always ridden with Legolas.
Then Legolas repaid his promise to Gimli and went with him to the Glittering Caves; and when they returned he was silent, and would say only that Gimli alone could find fit words to speak of them. “And never before has a Dwarf claimed a victory over an Elf in a contest of words,” said he. “Now therefore let us go to Fangorn and set the score right!” - Lord of the Rings, Many Partings
Gimli was right about the Glittering Caves, and Legolas finally understands their beauty. The competitive aspect of their friendship is highlighted again, as Legolas is eager to “set the score right!”
But all save Legolas said that they must now take their leave and depart, either south or west. “Come, Gimli!” said Legolas. “Now by Fangorn’s leave I will visit the deep places of the Entwood and see such trees as are nowhere else to be found in Middle-earth. You shall come with me and keep your word; and thus we will journey on together to our own lands in Mirkwood and beyond.” To this Gimli agreed, though with no great delight, it seemed. - Lord of the Rings, Many Partings
Legolas cannot wait to explore “the Entwood”, but Gimli is not too thrilled about it.
Gimli Glóin's son is renowned, for he was one of the Nine Walkers that set out with the Ring; and he remained in the company of King Elessar throughout the War. He was named Elf-friend because of the great love that grew between him and Legolas, son of King Thranduil, and because of his reverence for the Lady Galadriel. 
Here follows one of the last notes in the Red Book: 
We have heard tell that Legolas took Gimli Glóin's son with him because of their great friendship, greater than any that has been between Elf and Dwarf. If this is true, then it is strange indeed: that a Dwarf should be willing to leave Middle-earth for any love, or that the Eldar should receive him, or that the Lords of the West should permit it. But it is said that Gimli went also out of desire to see again the beauty of Galadriel; and it may be that she, being mighty among the Eldar, obtained this grace for him. More cannot be said of this matter. - Lord of the Rings, Appendix A 
Fo.A. 120: Then Legolas built a grey ship in Ithilien, and sailed down the Anduin and so over Sea; and with him, it is said, went Gimli the Dwarf. - Lord of the Rings, Appendix B
These two quotes (from Appendix A) are the ones that create the most confusion about Gimli's feelings. It is clear that they are written by an internal third party, likely someone in Gondor in the Fourth Age. The text of LotR itself shows the opposite – Gimli's love for Galadriel is far past reverence and admiration; it is deep and eternal, greater than any other love he had ever had. Indeed, his sailing is only rationalized by his love for Galadriel. While he and Legolas are good friends, their bond can never become close to the love he holds for Galadriel.

Also, we know there were great friendships between some elves and dwarves in the First and Second Ages – it is very likely that there were other friendships equal to, or greater than, Legolas and Gimli's. This fact does not make theirs any less true or deep.

I know many have also been confused over Gimli's fate – does he become immortal in the “Undying Lands”?

He does not:
And some there were who said: “Why should we not go even to Aman, and taste there, were it but for a day, the bliss of the Powers? Have we not become mighty among the people of Arda?” 
The Eldar reported these words to the Valar, and Manwë was grieved, seeing a cloud gather on the noontide of Númenor. And he sent messengers to the Dúnedain, who spoke earnestly to the King, and to all who would listen, concerning the fate and fashion of the world. 
“The Doom of the World,” they said, “One alone can change who made it. And were you so to voyage that escaping all deceits and snares you came indeed to Aman, the Blessed Realm, little would it profit you. For it is not the land of Manwë that makes its people deathless, but the Deathless that dwell therein have hallowed the land; and there you would but wither and grow weary the sooner, as moths in a light too strong and steadfast.” - The Silmarillion, The Akallabêth
The passing 'oversea', therefore, of Mortals after the Catastrophe - which is recorded in The Lord of the Rings - is not quite the same thing. It was in any case a special grace. An opportunity for dying according to the original plan for the unfallen: they went to a state in which they could acquire greater knowledge and peace of mind, and being healed of all hurts both of mind and body, could at last surrender themselves: die of free will, and even of desire, in estel. - Morgoth's Ring, Athrabeth Finrod ah Andreth, Author's Note 4

I hope my essay has helped you understand the complicated history between the elves and the dwarves. There is certainly a lot of food for thought here, and we once again see one of Tolkien's main themes – that isolationism is bad and that good comes from seeing the good in others and banding together – reflected throughout all of elven and dwarven history.

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