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1.3 Polonius tells his son, "To thine own self be true," and commands his daughter not to be promiscuous.
2.1 Ophelia tells Polonius that Hamlet is acting weird; Polonius concludes Hamlet is crazy because he's been denied love, or just drunk.
2.2 Polonius tells Gertrude and Claudius about his "mad with love" theory and proposes a plan. He tries to assess the Prince's madness and is called a "fishmonger" in the process, among several other insulting names. He then watches the players perform the Hecuba speech and remarks that it is "too long."
2.3 Polonius drags his daughter before the King and Queen, sticks a prayer book in her hand, and tells her she's the bait for Hamlet. He then does what he always does, and hides behind a curtain. Hamlet's interaction with Ophelia does not support the mad love theory, yet Polonius still thinks he's right.
3.2 Polonius watches the play and says little. Hamlet mocks him… yet again.
3.3 He makes a plan with Claudius to overhear the interaction between Gertrude and Hamlet.
3.4 Polonius hides behind an arras to hear what Hamlet has to say. He tries to emerge from the curtain when Gertrude calls for help, but ends up getting stabbed by Hamlet instead. Polonius's last line: "O, I am slain!"