Boku no Hero Academia

Boku no Hero Academia (or My Hero Academy) is a manga which follows the story of Midoriya, a 14 year old boy who dreams of becoming a hero, which drives him to apply to Yuuei High, a popular high school where those who wish to become heroes go in order to gain the necessary qualifications to become pros. However, although he has been studying for the entrance exams, Midoriya has no 'individuality', something which others seem to have, enabling them to become a hero or villain. But with the help of All Might, a popular hero, Midoriya strives to fulfill his dream and become a hero to save people through training and All Might's quirk - one which allows him to transfer his powers to another person.

This is the first time that I have read this type of manga, and I must say that it is quite a steady paced story, but is interesting nonetheless.
Midoriya has the same motivation and drive as other well known characters in the world of anime and manga (think Naruto and his dream of becoming Hokage), and naturally this comes with a backstory, people who say that he'll never make it because of who he is and the small group who support him. This means that his potential is often underestimated by others, which you first see when he goes for the entrance exams for Yuuei. But things soon turn around for Midoriya when he passes the exams and gets into Yuuei.

If this interests you, I must warn you of the first chapter (chapter 0). This seems to be an entirely different story but features Midoriya, who seems to be a salesman for a company selling gadgets to heroes. I read this and didn't really get into it, but luckily all but the main character and world of heroes was changed.

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Summary:

A boy dreams of becoming a hero and is given the chance to fulfill his dream by a popular hero