Kamunagara

Kamunagara: Rebirth of the Demonslayer (カムナガラ, Kamunagara), is a manga by Hajime Yamamura.

Plot
Hitaka Kugaya, a former kendo champion who often has a weird recurring dream about a mysterious woman, seems to be the only one in his class who's not interested in Takemi Kanata; he meets her in the music room, while she's playing Beethoven's Tempest, and she warns him that a tempest is coming.

While going back home from school, he's followed by a dog, and when he gives him something to eat it opens a huge mouth, revealing itself as a demon. At the very last moment, when his hand is already in the dog's mouth, in it appears a sword (the holy sword "Himuka"), which splits the beast in half; after that, Takemi appears, and gets rid of the body with a strange mirror ("mirror of containment"). Crying, she calls him Tohma, and reveals him that the beasts are "invaders from another world", and they're "guardians of the seal": the two worlds are separated by a seal, but the seal gets breached periodically, and the clan of the sword has the mission to stop the invasion.

At first he doubts Takemi's words, as he doesn't remember anything, but when he comes back home he finds his aunt murdered by a crow demon, and he's badly injured; when he awakes in a hospital, there's already no way out for him.