Claudius is Hamlet's uncle (and former King Hamlet's brother). He creates the conflict of the play by murdering his brother and taking the throne from Hamlet.    

Claudius is aware Hamlet has it out for him, and knows that Hamlet's erratic behavior is not insanity, but an act. In this way, he is one of the wisest characters of the play. He is, however, rotten, not even praying for forgiveness for murdering his brother despite realizing it was a bad thing to do. He even married his brother's widowed wife (much to the dismay of Hamlet, who calls him his "uncle-father")!  

Claudius in the 1996 film. As king, he has the best-looking outfits (this one not included)!