Toumei Ningen Kyoutei

Kyoubei Kurokawa, university student, has an aimless life. Having run away from home to live alone he doesn't even have a place to sleep. One day he was saved from falling off a bridge by Asumi Nanjou, a mysterious girl from the same university, that takes him to her apartment to treat his wounds. When she finds out about his situation, Nanjou decides to let him live on her house, on one condition: he'll be an invisible man. Bewildered at first, he later finds out what she meant: she'll completely ignore his existence. Meet Kurokawa and discover the advantages (and disadvantages) of being an invisible man and unravel the mysteries behind Asumi Nanjou.

(Source: MangaDex)