Discuss the importance of Claudius in the play.
Claudius is the villain of the play. In particular, he plays several villain archetypes: he is a tyrant who wants power at any price; he is a traitor who betrays those who trust him most; he is a backstabber who delights in duping the unsuspecting, who relishes in his victims' secrets; he is a schemer, a spy who plots the ruin of others.
Above all, he commits the most heinous crimes imaginable: incest, regicide, patricide, and fratricide. He kills his King, his brother, his wife the Queen, his nephew the Prince. He uses a whole family of pawns (Polonius, Ophelia, and Laertes) to do so, and they die also. In the end, two families are dead because of Claudius. Norway is defeated and invaded because of Claudius.
Claudius is based on the chieftain Feng from the Saxo Grammaticus and the Roman archetypal Claudius I, who also committed incest.
Claudius is not without remorse. He tries to confess his sin and even comments on his guilt in Act III: "O, my offence is rank it smells to heaven"