The Noldor (meaning those with knowledge in Quenya) are Elves of the Second Clan who migrated to Valinor and lived in Eldamar. The Noldor are called Golodhrim or Gódhellim in Sindarin, and Goldoi by Teleri of Tol Eressëa. The singular form of the Quenya noun is Noldo and the adjective is Noldorin.  They were the Second Clan of the Elves in both order and size, the other clans being the Vanyar and the Teleri. Like the Teleri, they typically had grey eyes and dark hair (except for those who had Vanyarin blood, most prominently the members of the House of Finarfin).
The Noldor were very tall and of muscular build. Their hair colour was usually very dark brown (according to Tolkien, Elves did not have absolute black hair), but red and even white ("silver") hair exist among them too. Their eyes were usually grey or dark.
The most distinctive thing about Noldorin culture was their fondness for the crafts. This ranged from jewelry to embroidery to the craft of language. They had great pride in this art; the unfortunate side effect of this was an arrogance that plagued the Noldor and later caused them great suffering. The Noldor were also more fond of living in and building big cities than the Vanyar, Teleri and Avari. Their cities were usually located in deep mountain valleys, as opposed to the shore and woodland homes of the Teleri and the Vanyar's sharing of the homes of the Valar. They had domesticated horses and dogs.
Second and Third Ages
Most of the Noldor sailed back to Aman at the End of the First Age; but some, like Galadriel (daughter of Finarfin) or Celebrimbor (grandson of Fëanor), refused the pardon of the Valar and remained in Middle-earth. Gil-galad founded a new kingdom at Lindon, and ruled throughout the Second Age, longer than any of the High Kings except for Finwë. He was also accepted as High King by the Noldor of Eregion.
But after a while Sauron had replaced his master Morgoth as the Dark Lord. With the aid of the Ruling Ring he fortified Mordor and began the long war with the remaining Elves. He attacked Eregion, destroying it, but was withstood in Rivendell and Lindon. With the aid of the Númenóreans, the Noldor managed to defeat him for a time. However, in the year 3319 of the Second Age Númenor fell due to Ar-Pharazôn's rebellion against the Valar, in which Sauron had a great part.
When Elendil with his sons escaped to Middle-earth and established the realms of Arnor and Gondor, Sauron tried to conquer Gondor before it could take root. Both Elendil and Gil-galad set out for Mordor in the Last Alliance of Elves and Men and defeated Sauron in the Battle of Dagorlad and finally in the Siege of Barad-dûr, marking the end of the Second Age. There Gil-galad perished, and so ended the High Kingship of the Noldor. No new High King was elected, as no one claimed the throne; for this reason, the High Kingship of the Noldor was said to have passed overseas, to the Noldor of Valinor, ruled by Finarfin, the third son of Finwë who had never left. In Middle-earth of the descendants of Finwë only Galadriel and Elrond Half-elven remained (and the Númenórean Kings through Elrond's twin brother Elros).
In the Third Age, the Noldor in Middle-earth dwindled, and by the end of the Third Age the only big communities of Noldor remaining in Middle-earth were in Rivendell and Lindon. Their further fate of fading utterly from the World was shared by all Elves as the Third Age ended.
Noldor of Eregion
The origins of Eregion are not entirely clear, but it seems to have been originally settled by Galadriel and Celeborn during the eighth century of the Second Age. There were Elves other than the Noldor in that land, but it was that people who had the deepest interest in the crafts of making, and a great friendship grew between the Noldor of Eregion and the Dwarves of nearby Khazad-dûm. For more than six hundred years the new land remained at peace in the western shadows of the Misty Mountains.
After that time a powerful figure naming himself Annatar came to Eregion. Galadriel rejected his friendship, but he had immense knowledge, and his influence over the jewel-smiths grew, and especially over one Celebrimbor, a grandson of Fëanor. Galadriel and Celeborn passed into the east at this time, to settle in the land that would become Lórien, leaving Celebrimbor to become Lord of Eregion.
Under Annatar's guidance, the jewel-smiths of the Gwaith-i-Mírdain began the making of Rings of Power. Of these Rings, Three were made outside the influence and knowledge of Annatar, and so the Elves discovered that their teacher had been Sauron himself, enacting a plan to enslave them through his One Ring. Enraged at being discovered, Sauron sent a force of war into Eriador, overwhelming Eregion and bringing an end to all its people.
A note on the language of the Elves
- Tolkien originally imagined that the language which would become Sindarin was spoken by the Ñoldor (second clan of Elves). However, Tolkien later decided that it was the language of the Sindar. For this reason it is called Noldorin in the older material, such as the Etymologies. When Noldorin became Sindarin, it also adopted some features of the originally unrelated language Ilkorin. Tolkien based the sound and some of the grammar of his Noldorin/Sindarin on Welsh, and Sindarin displays of the consonant mutations that characterise the Celtic (especially Brythonic) languages. The language was also probably influenced to an extent by the Germanic languages, as Tolkien was a scholar of both Old English and Old Norse.
- J. R. R. Tolkien in his later works usually employed the spelling Ñoldor, with a tilde over the first letter. This was his notation for the pronunciation of the name in the First Age (beginning with the final sound of English sing); in the Third Age in The Lord of the Rings and The Silmarillion the spelling Noldor was introduced.
- J.R.R. Tolkien, "Changes Affecting Silmarillion Nomenclature", Parma Eldalamberon 17, p. 125