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...