Known as『とある魔術の禁書目録』or とあるまじゅつのインデックス.
The story is set in Academy City , a technologically advanced Academic city located at western Tokyo which studies scientifically advanced superhuman students with powers, but is also set in a world where magic is real. Tōma Kamijō is a student in Academy City whose right hand, the Imagine Breaker, has the ability to negate any supernatural powers, but also his own luck.
One day he finds a young girl hanging on his balcony railing named Index. She is a nun from Necessarius, a secret magic branch of the Church of England, and her mind has been implanted with the Index Librorum Prohibitorum—103,000 forbidden magical books the Church has removed from circulation. His encounter with her leads him to meet others from the secret world of science and magic and an adventure with his friends where science and magic collide. Tōma's unusual power places him at the center of conflicts relating magicians and science-based espers in Academy City. As Tōma tries to help and protect his friends, he learns the people he knows are not as they appear and begins to attract the attention of magicians and espers alike as they try to unravel the secrets of Academy City and Index.

Source:Wikipedia