Though this be madness, yet there is method in’t. (II.II.204-205)
This quote is significant to the play because Polonius says it in aside, mid-conversation with Hamlet. He is listening to Hamlet speak, and thinks that though his descriptions are a little outrageous, they do in fact make sense. Polonius does not realize, however, that Hamlet is making fun of him, and therefore Hamlet is proving that he can act mad and still have his way with the other characters of the play, without them realizing it.
Hamlet: How is it with you, Lady?
Queen: Alas, how is it with you... (III.IV.117-126)
This quote is significant to the play because it shows us that Hamlet is possibly becoming more and more insane. When the ghost enters Gertrude’s bedchamber and starts talking to Hamlet, Gertrude cannot see the ghost; just the doorway, thus freaking her out and leading her to think that her song might be mad, though she was reluctant to believe it before.
That I essentially am not in madness but mad in craft. (III.IV.189-190)
This quote is significant to the play because Hamlet is speaking to Gertrude in her bedchamber, about her marriage to Claudius, just having killed Polonius minutes before. After he murders Polonius, Hamlet vents to his mother and urges her not to return to Claudius’ bed. In midst of this, he says this line, almost as a last attempt at hinting to his mother that he’s not crazy though his actions deem him so.