Jumper

Steven Gould's SF classic, Jumper.

Davy can teleport. He first discovers his talent during a savage beating delivered by his abusive father, when Davy jumps instantaneously to the safest place he knows, his small-town public library. As his mother did so many years before, Davy vows never to go home again. Instead, he sets off, young and inexperienced, for New York City.

Davy gradually learns to use and control his powers, first for sheer survival in an environment more violent and complex than he ever imagined. But mere survival is not enough for Davy. He wants to know if his mother disappeared so completely from his life because she, too, could Jump. And as he searches for a trace of anyone else with powers like his own, he learns to use his abilities for more than escape and theft.

A young man with nothing to lose, and the ability to go anyplace he wants, can help a lot of people. But he can also make a lot of trouble, and sooner or later trouble is going to come looking for him. The one way Davy can think of to locate others who can Jump is to make himself visible to them, but if he does, the police will surely find him too.