He makes fun of Polonius, calling him a fishmonger, and saying he is old, ugly, etc. While Hamlet says this, Polonius is unaware that it is directed towards him. Polonius takes it as madness, and believes the quotes are coming from a book Hamlet is reading. I believe Hamlet is just having fun with his "madness." He wants people to believe he is mad, but while doing so he wants to tell them .
how he feels about them without letting them know what he is saying. He wants to mock them. Hamlet knows exactly what he is doing. Now that everyone is sure of his madness, he wants to put truth in it. These are some clues that Hamlet is not mad. To the other characters in the book he may look insane, but because we, the audience, know what is happening, and know about Claudius killing the old king, Hamlet's actions seem justified. I believe that if the audience had no real connection to what Hamlet knew, then yes, he would seem mad, but because we do know, why is there a question of his madness? Hamlet also confesses to himself that he is upset because he wants to revenge his father, but is procrastinating. If indeed he was mad, he would not still be thinking such rational thoughts. Hamlet is also on to the new king, and his ways of trying to rid Denmark of Hamlet. Hamlet still acts mad, but tries to get the guiltiness out of Claudius. A mad person would not do this. A mad person would just kill the person who murdered their father and not try to find justice and reason. Hamlet is still thinking, still pondering and organizing. This is not the mind of a mad person.
Hamlet does take his madness a bit too far at times. He really does love Ophelia, but because he convinces her he does not, it makes her just as mad as everyone thinks he is. He tells her, "I loved you not." "Get thee to a nunnery!". (Hamlet, pg. 141). Besides fooling people of his madness, Hamlet also wants revenge. He is so tired of putting off killing Claudius that one day when talking to his mother, he hears something behind the curtain and stabs it, thinking it's Claudius, when really it is Polonius.