Eragon I was an elf and the first ever Dragon Rider in the history of Alagaësia. He became a historic hero who helped to end the devastating war raging between the dragons and elves. He was the first Dragon Rider and was the order's first leader. His dragon, Bid'Daum and another unnamed white dragon, united the dragons and elves, helping to end Du Fyrn Skulblaka. This is one of the many reasons why the Riders were treasured throughout the land: if not for Eragon I and Bid'Daum, the elves and the dragons might have driven each other to extinction in Alagaësia.
After the elves arrived in Alagaësia, a young elf hunted and killed a dragon. This resulted in the dragons killing the elf, but that did not satisfy the dragons' fury and they attacked the whole elven nation. During this time, a dragon egg was left deserted, for an unknown reason, although there are suspicions that either the dragons parents had been killed or that the egg had been intentionally left there. An elf named Eragon found the egg and when the dragon hatched, he took care of it. Once the dragon - who Eragon named Bid'Daum - grew large enough, they traveled across the land, making peace between both races and finally, ending the war. After the war, Eragon, Bid'Daum and the nameless leader of the dragons formed the Dragon Riders. It is known that Eragon once sat for dwarf artisans in Celbedeil, where many years later, the new rider of the same name, Eragon Shadeslayer, was able to see his likeness. The fates of Eragon and Bid'Daum are unknown at this time.
It is said that the name "Eragon" carries power and that it is rarely given. While it is not known why this is so, the most likely reason would be simply that it was the name of the first Dragon Rider, a significant person in the history of Alagaësia. If that is so, then presumably in the time of the first Eragon the name was quite ordinary and common, although perhaps only among the elves.
As the Leader of the Riders, Eragon was the most powerful of the elite order. Eragon was an extraordinarily gifted swordsman with amazing speed,strength and magic. It is possible that he was not as powerful as some future leaders of the dragon riders by him being of an ancient time before some advancements had been made despite having a wild-rider dragon.