Motivation and Irony of Situations in "Hamlet"

In the play "Hamlet", Hamlet's father, the king, is killed by Claudius. Claudius is the former king's brother, so as a result, he takes the throne. He also marries Hamlet's mother, the queen. Hamlet's father appears one night as a ghost and speaks to Hamlet. He tells Hamlet that Claudius murdered him and asks his son to seek revenge, by killing his murderer.
During one scene in the book, after 'Mousetrap' (a play within the play) has taken place, Hamlet is talking with his mother concerning the fact that she has married her dead husband's brother. Hamlet is devastated over this and feels h…