Hamlet is the son of the King of Denmark . When Hamlet 's father dies , his uncle Claudius becomes king and marries Hamlet 's mother ( Gertrude ) . The play , set in the Kingdom of Denmark , recounts how Prince Hamlet exacts revenge on his uncle Claudius for murdering the old King Hamlet ( Claudius 's brother and Prince Hamlet 's father ) and then succeeding to the throne and marrying Gertrude ( the King Hamlet 's widow and mother of Prince Hamlet ) .