‘World of Narue’
After school on a rainy day, eighth-grader Kazuto Iizuka’s heart is stolen by a girl with a mysterious way of talking and acting. Her name is Narue Nanase. The problem is, she seems to be an alien. Her personality is that of someone who seems destined to a life of poverty and her special power is teleportation. Kazuto confesses his love to her and their relationship begins. But, as expected of an alien, Narue is surrounded by strange people, if they could be called that. Kazuto’s life suddenly becomes a series of odd events.
Descriptions taken from AniDB.net