The Second Kindred of the Eldar to follow Oromë from Cuiviénen to the relative safety of Valinor, led by Finwë. Beloved of Aulë, they delighted in making things by hand. The Noldor built Tirion upon Túna (in the Calacirya) where they dwelt with the Vanyar. Nearly all of the Eldar that appear in the works of J.R.R. Tolkien are Noldor.
The greatest craftsman of all the Noldor was Fëanor, son of Finwë. Although Elves do not die of old age, giving birth to Fëanor ...used...up... his mother Miriel, and she went to dwell in the halls of Mandos. Finwë later wed Indis of the Vanyar who bore him Fingolfin and Finarfin.
The greatest creations of the greatest craftsman of the Noldor were the Silmarils, three gems in which Fëanor captured the light of the Two Trees.
After the release of Melkor from the three ages of his chaining, he came to live in Valinor. He shared secrets of creating wonderful things with the Noldor, which made them susceptible to the discontent against the Valar which he whispered in ther ears at the same time, priming the Noldor for their revolt.
Although Melkor did indescribable evil by slaying Finwë, poisoning the Two Trees, and stealing the Silmarils, Fëanor and his sons made sure this evil would consume the Noldor by swearing their terrible oath. The Oath compelled them to follow Melkor back to Middle-Earth, precipitating the worst of their deeds: the Kinslaying of Alqualondë where they killed the mariners of the Teleri in order to steal their ships for transport across the sea. Although a few Noldor (led by Finarfin) turned back after the Kinslaying, the rest of them followed Fëanor, sharing his exile.
Understanding the travails the Noldor underwent in Middle-Earth is best experienced by reading The Silmarillion. However, suffice it to say that unnumbered tears were shed, and the Oath wrought a considerable amount of added misery. By the end of the First Age, all of the leaders of the revolt were dead (except Galadriel) and the remnants of the Noldor were led by the great-grandchildren of Finwë, Celebrimbor and Erenion.
The Valar lifted the Noldor's exile (except for Galadriel) and most of them took the opportunity to sail back to Aman. A few remained behind: Erenion, aka 'Gil-Galad' was High King of the Noldor, and Celebrimbor set up the realm of Eregion. But one by one the Noldor sailed West or were killed. Eregion was destroyed by Sauron during the Second Age, and Gil-Galad was slain along with with Elendil as they vanquished Sauron at the Second Age's end. By the time of the Lord of the Rings, the Noldor remaining in Middle-Earth were very few indeed. When Galadriel was finally allowed to sail West after the downfall of Sauron, it is quite possible that the last Noldor sailed with her.