The main characters in Hamlet are as follows:
Hamlet: He is a tortured soul, grieved over his father's death and his mother's quick remarriage (to his uncle!). He becomes especially tormented when the ghost of his father appears and demands he avenge his murder by killing Claudius.
Claudius: Claudius, ambitious for the throne, cold-bloodedly murders his brother and marries his brother's wife. He doesn't regret this, as he likes the power he has and is glad to be married to Gertrude. He realizes that his biggest threat is Hamlet and works to have him killed.
Gertrude: She will confess to the frenzied Hamlet that she probably was wrong to marry Claudius, but she nevertheless remains loyal to her husband, not realizing how evil he is. Some critics believe that an Oedipal desire for his mother, enacted by Claudius, drives Hamlet's loathing of Claudius.
Polonius: A wordy and pompous but sly courtier, he tries to please Claudius by finding out what is wrong with Hamlet. He gets accidentally killed by Hamlet for his efforts.
Laertes: Polonius's son and, in many ways, a "mirror" of Hamlet, Laertes comes home determined to avenge his father's death by killing Hamlet. Because he can't control his emotions, he is used by Claudius.
Ophelia (Laertes's sister), Horatio (Hamlet's friend), and the ghost are more minor characters, but they play important roles: Ophelia's suicide adds to Laertes's rage against Hamlet; Horatio is the voice of reason and the survivor who will tell the story of what went wrong in the Danish court; and the ghost sets the action of the play in motion with his revelations.