Hamlet is the main protagonist of this play. The heir to the throne in Denmark, Hamlet is the son of the late King of Denmark and Queen Gertrude along with being the nephew of the present King, Claudius. Hamlet displays a variety of emotions throughout the play, but perhaps he is most simply characterized by bitterness, a sense of gloom and revengeful towards his uncle, Claudius, who took the throne after his father died and married his mother. Hamlet is well-educated, having studied at the University of Wittenberg with his friends Rosencrantz, Horatio and Guildenstern, although he doesn't always use this education to his advantage. Instead, he tends to make rash decisions, often on an impulse. This impulsive nature of Hamlet is shown perhaps most represented in his ordeal with Ophelia, where he went into her room and stared at her with his "doublet all unbraced, no hat upon his head, his stockings fouled, ungartered and down-gyved to his ankle, pale as his shirt, knees knocking together and with a look so piteous..." (Act 2 Scene 1, Lines 87-94).
Polonius is the father of both Laertes and Ophelia, whom Hamlet listed for at the beginning of the novel but fell out of love with after he assumed that he was telling her to withhold her love from him. Polonius is characterized as being very sneaky, coniving and manipulative throughout the novel, as shown by his multiple plans throughout. Perhaps the best example of him being a sneaky, coniving person is shown in his plan to see what exactly Hamlet thinks of his daughter and why he is acting weird, telling her to "read on this book," where he knows Hamletoften walks (Act 3 Scene 1, Lines 49-51) while he eavesdrops on the conversation that they are going to have. Polonius' downfall is brought upon him by this same type of attitude, though, as he is killed by Prince Hamlet while he is spying on a conversation between him and his mother, Queen Gertrude, in Act 4.
King Claudius is the main antagonist of this play and the uncle of Prince Hamlet. Claudius poisons Hamlet's father, the late King Hamlet, and kills him beforr winning over the now-widowed Gertrude and marrying her to take the throne. To the outside observer, Claudius would seem like a very fine person and an even better King - sending ambassadors to Norway early on in the novel when he first becomes King. To Hamlet and those who know him well, though, he is a much different person. Perhaps the ghost of the late King Hamlet sums up Claudius the best, calling him "what is rotten with Denmark," after calling him an "incestous beast" (Act 1 Scene 5 Lines 42-43). Claudius is also portrayed as a somewhat persuasive person, shown mostly through him winning over Queen Gertrude after her first husband's death. even being mentioned by Hamlet as wooing her with the "witchcraft of his wit" (Act 1 Scene 5 Line 47). Claudius overall represents somebody that nobody wants to grow up to be, as he is controlled by greed, power and lust instead of his conscience.
Queen Gertrude is the mother/aunt of Hamlet and was married to the late King Hamlet before re-marrying his brother and Hamlet's uncle, Claudius. While Gertrude knows that marrying Claudius displeases Hamlet, she does such anyways. Although she expresses regret for this later in the novel, saying that "thou turn'st my very eyes into my soul, and there I see such black and grained spots as will not leave their tinct" (Act 3 Scene 4 Lines 88-91). Gertrude for the most part seems to be oblivious to the whole situation and the Ghost reveals to Hamlet later in the story that she isn't to blame for his killing, stating instead that she will be judged when her time comes and that Claudius is the real villian. Gullible, easily manipulated and foolish sum up Queen Gertrude perfectly according to her actions throughout this play.
Ophelia is the daughter of Polonius and is also Hamlet's muse throughout the play. Hamlet makes several attempts to declare his love for her, such as sending her love notes and proclaiming to her that he does. Ophelia also likes Hamlet, but her father Polonius believes that Hamlet is just going to use her. Ophelia remains loyal to her father and doesn;t pursue a relationship with Hamlet, displaying one of the more pronounced characteristics for a character that is overall somewhat murky: loyalty. She is loyal to her father until the very end, obeying him to stay away from Hamlet even when she gets obviously very depressed towards scene 4 and starts writing songs about love and destruction. Ophelia is eventually done in by her own madness, torn between Hamlet and her father, she drowns herself in a river.