My Hero Academia

In a world where almost everyone manifests a Quirk by age four, Izuku Midoriya is one of the rare children who never does. He has spent his life cataloguing other people's powers in notebooks and his crush on a hero career mostly in private. An encounter with All Might — the country's reigning Symbol of Peace — turns into the offer of a lifetime: All Might has been searching for an inheritor for his own Quirk, One For All, and Izuku's selflessness in a brief crisis convinces him he has found one. The manga is Izuku's training under All Might and his enrollment at U.A. High School.