Beyond the Boundary (境界の彼方, Kyoukai no Kanata) is a Japanese light novel series written by Torii Nagomu, with illustrations by Kamoi Tomoyo.
It won an honorable mention in the Kyoto Animation Award competition in 2011. An anime adaptation by Kyoto Animation aired from October 2, 2013 to December 18, 2013.
As for the plot, it starts with a rather abrupt scene. High school student Kanbara Akihito goes to save his classmate Kuriyama Mirai from committing suicide, and suddenly she draws her sword and stabs him, to discover he is immortal. A rather abnormal start for an anime, if you ask me!
After learning that Mirai is a Spirit World Warrior (異界士, ikaishi) – specialists who protect humans from being affected by youmu (妖夢, lit. dreamshades) – and the last surviving member of her spirit hunting clan, their lives become intertwined as Akihito seeks to help Mirai gain the confidence to kill youmu so that she may stop attempting to kill him as practice.