Kyuta, a boy living in Shibuya, and Kumatetsu, a lonesome beast from Jutengai, an imaginary world. One day, Kyuta forays into the imaginary world and, as he's looking for his way back, meets Kumatetsu who becomes his spirit guide. That encounter leads them to many adventures.
Teenage math whiz Kenji Koiso agrees to take a summer job at the Nagano hometown of his crush, Natsuki. When he arrives, he finds that her family have reunited to celebrate the 90th birthday of their matriarch. His job: pretend to be Natsuki's fiancé. Meanwhile, his attempt to solve a mathematical equation causes a parallel world's collision with Earth.
When 17-year-old Makoto Konno gains the ability to, quite literally, 'leap' backwards through time, she immediately sets about improving her grades and preventing personal mishaps. However, she soon realises that changing the past isn't as simple as it seems, and eventually, will have to rely on her new powers to shape the future of herself and her friends.