Half a King by Joe Abercrombie

Betrayed by his family and left for dead, prince Yarvi, reluctant heir to a divided kingdom, has vowed to reclaim a throne he never wanted. But first he must survive cruelty, chains and the bitter waters of the shattered sea itself - all with only one good hand. Born a weakling in the eyes of a hard, cold world, he cannot grip a shield or swing an axe, so has sharpened his mind to a deadly edge. Gathering a strange fellowship of the outcast, he finds they can help him more than any noble could. Even so, Yarvi's path may end as it began - in twists, traps and tragedy.