While it would seem that she did not love her husband, but it really seems like Gertrude marries Claudius so quickly because she knows it is the only way to preserve her status and position in the kingdom, otherwise she will lose power, rank, and privilege. She needs a man to protect her, and she uses Claudius to save herself, just as Claudius uses her to ensure he can take over the kingdom.

It seems by the end of the play that Hamlet is truly insane. He talks to dead skulls, he reacts irrationally (such as when he stabs Polonius even though he cannot even see it is really him through a curtain), and he plots revenge on his uncle, but cannot bring himself to carry it out until his own mother dies. He seems extremely depressed and cynical, and he just seems mad. He is not acting, there would...
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