The story is set in a world where supernatural powers exist through science, and magic exists through religion.
In the story, Touma Kamijou is an ordinary high school boy with terrible academic scores and a power called Imagine Breaker. Imagine Breaker can defeat any other power, but it also undermines Kamijou's own good luck. His Imagine Breaker's immense strength is literally immeasurable, so hapless Kamijou is listed at the supernatural level of 0. He happens to meet a girl in white hanging off his window balcony. The girl says she is being chased by sorcerers, and Kamijou learns that the girl is a Church of England nun whose memories have been forcibly replaced by Index-Librorum-Prohibitorum — the 103,000 forbidden texts of the Church.