Elfstone
A famous green jewel that Galadriel gives as a gift to Aragorn just before the Fellowship of the Ring leaves the wood of Lothlórien: This stone I gave to Celebrían my daughter, and she to hers; and now it comes to you as a token of hope. In this hour take the name that was foretold for you, Elessar, the Elfstone of the house of Elendil![5]
This stone, worn by Aragorn, later causes him to also be given the name of Elessar by the people of Minas Tirith. It appears in The Lord of the Rings.
Tolkien also calls it the Elessar or the Stone of Eärendil and describes it as being set in an eagle-shaped silver brooch.
There are a variety of stories about the jewel's origin in Unfinished Tales: There was in Gondolin a jewel-smith named Enerdhil, and he was the greatest of that craft among the Noldor after the death of Fëanor...it came into his heart to make a jewel within which the clear light of the sun should be imprisoned, but the jewel should be green as leaves. And he made this thing, and even the Noldor marvelled at it. For it is said that those who looked through this stone saw things that were withered or burned healed again or as they were in the grace of their youth, and that the hands of one who held it brought to all that they touched healing from hurt.[6]
The gem was then given to Idril the fairest in Gondolin and she in turn gave it to her son Eärendil and he takes it to Valinor and never returns.
Here the "Enerdhil-story" diverges into two versions:

• Gandalf brings back the jewel from Valinor and gives it to Galadriel, as a token from Yavanna that the Valar have not forsaken Middle-earth. In this version Gandalf also remarks prophetically to Galadriel that she will only hold it for a little while, before she passes it to another, who will also be called Elessar.

• Galadriel is pained at the state of Middle-earth and wants something to help heal its wounds. Celebrimbor, who is in love with Galadriel, remakes the jewel as her behest. It is interesting to note that Celebrimbor was also in Gondolin in the time of Enerdhil and learned much from him. Although we are more familiar with Celebrimbor (and his Rings of Power), he was actually overshadowed by the superior skill of Enerdhil, who was second only to Fëanor.

There is also a third version that differs greatly from the first two. In that there is no mention of Enerdhil and instead it was Celebrimbor himself who in Gondolin made the original jewel. Eärendil takes this jewel to Valinor forever and in the Second Age Galadriel asks Celebrimbor to remake the jewel again.
Another version states that the Elfstone was created by Fëanor, who gave it to his eldest son Maedhros as he died. Maedhros then gave it to Fingon as a token of friendship, but the whereabouts of the gem thereafter are not known. The dragon-helm of Azaghâl probably replaced the Elfstone as Maedhros's gift to Fingon.
All versions end with the jewel in Galadriel's possession. She then gives it to her daughter Celebrían, who in turn gives it to Arwen. It nonetheless is in Galadriel's keeping in Lothlórien before she passes it on to Aragorn. According to Tolkien, this also held the function of a wedding gift from the family of the bride to the groom.
Another point of note is that earlier in The Lord of the Rings, Aragorn urged Bilbo Baggins to include a green jewel in a poem about Eärendil he was composing, possibly anticipating the symbolic importance that the gem would have in his life. Bilbo, obeying Aragorn but seemingly unaware of the Elfstone's story, included an inaccurate reference to an emerald.[7]