The Tuatha'an, (pronounced: too-AH-thah-AHN), also known as "Traveling People" or "Tinkers," live by a pacifist philosophy they call the Way of the Leaf.
The Tuatha'an were originally Da'shain Aiel who followed the Way of the Leaf. After the Aiel were repeatedly attacked by bandits, Sulwin and several others of the Aiel defied Adan, then leader of the Jenn Aiel. They abandoned the items of the One Power entrusted to them by the Aes Sedai and took their wagons in search of the "song" (may refer to the prologue of "The Eye of the World", in which the mad Lews Therin asks Ishamael if he has "the Voice" so as to participate in "the Singing"). This group became the Tuatha'an.
The Tuatha'an are one of the few peoples allowed passage through the Aiel Waste, perhaps because the Aiel cannot bring themselves to interact with such a strange people, although it seems more likely that the Wise Ones and clan chiefs know of their mutual origins and refuse to allow the Aiel near the Tuatha'an.
The Way of the Leaf defines how the Tuatha'an interact with outsiders. Tuatha'an will never do any violence, be it in anger or self-defense, not even to save their own life or that of another. If they feel that violence or physical confrontation may ensue, they will simply hide or leave the area. They also do not stay near areas where population is concentrated, as there is a greater propensity for violence in larger settlements. Their beliefs and actions frequently earn them repudiation by common folk.
The Tuatha'an have a bad reputation throughout the land. They are considered habitual thieves and, though they do not actively recruit new members, are often accused of trying to convert children to the Way of the Leaf.
Tinker Aes Sedai are also very rare as very few Tinker children wish to channel, as then they must become Aes Sedai and break from the Way of the Leaf.
The search for their lost song was the primary goal of the Tuatha'an by the time of the events in the series. It has been theorized that the song might have been known to Lews Therin Telamon and thereby to Rand Al'Thor, and it has likewise been suggested that the Aiel could have learned the song through the use of the pillars ter'angreal at Rhuidean. While this could potentially be true, co-author Brandon Sanderson responded on his personal Facebook page to the question of whether the Tuatha'an ever discovered their lost song. He responded, "[Robert Jordan] said specifically this was something that did not happen, at least not in the scope of the novels." (February 4th, 2013)
The name Tuatha'an comes from the Tuatha De Danann in Irish legend, who were a race of people who settled in Ireland. This reflects their wandering status in the Wheel of Time. The name of the only known Tuatha'an Aes Sedai, Aisling Noon, strongly resembles the Old Irish Aislinge Óenguso, the Dream of Angus, one of many myths in a series known as the Mythological Cycle.
Their culture and reputation is also strongly reminiscent of what, in Ireland, are also referred to as Tinkers. This, like in the books, is a slang term used for Irish Travellers. The name Tuatha'an translates from the Old Tongue as the Travelling People.
The origins of the Tuatha'an, and indeed the Aiel, within the books are similar to the story of Cain, who was condemned to spend his life wandering the earth until the Second Coming. In the Wheel of Time, the Second Coming is analogous to the rebirth of the Dragon and the coming of Tarmon Gai'don.
It is possible that the song is that which was sung the Ogier and the Da'shain Aiel shown to Rand in Rhuidean and that Loial rediscovered it in A Memory Of Light
The Tuatha'an are very similar to the real life Roma in both persecution with a reputation for being thieves and in that they live in wagons.