Boku dake no Madonna...and I love Her.

One day college student Suzuki Kyoichi finds an unknown woman lying in his bed. He gets to know that she's named Kataoka Surumi and seems to be the ex-girlfriend from a guy living in the opposite apartment. She says she got into Kyoichi's apartment in order to check out the woman for whom her former boyfriend dumped her. Therefore she starts living together with Kyoichi, who doesn't reject such a beautiful and charming girl, although she is a little bit older than himself. But as sudden as she appeared in front of Kyoichi, she one day disappears again without saying a word. What does all this mean?