Half a King by Joe Abercrombie (Shattered Sea #1)

Prince Yarvi has vowed to regain a throne he never wanted. But first he must survive cruelty, chains and the bitter waters of the Shattered Sea itself. And he must do it all with only one good hand.

Born a weakling in the eyes of his father, Yarvi is alone in a world where a strong arm and a cold heart rule. He cannot grip a shield or swing an axe, so he must sharpen his mind to a deadly edge.