Let not the royal bed of Denmark be
A couch for luxury and damnèd incest.
But howsoever thou pursuest this act,
Taint not thy mind, nor let thy soul contrive
Against thy mother aught. Leave her to heaven
And to those thorns that in her bosom lodge

These lines are the culmination of the instructions that the Ghost of Hamlet’s father gives to Hamlet for avenging his murder in Act 1, Scene 5. He tells Hamlet that the conniving Claudius the corrupted Gertrude before murdering him and turning the Danish king’s bed into a nest of incest. He commands Hamlet to kill his uncle, but to spare his mother, so that God can judge her and her own conscious will prey on her. The most famous phrase from this speech was used as the title for the 1944 bestselling novel Leave Her to Heaven and the classic 1945 film of the same name. The book and the movie center on a woman who, like Gertrude in Hamlet, is captivating as an individual, but who does terrible things.

You can read more about this quote in Quotes by Character: Gertrude (the second quote).

As I perchance hereafter shall think meet
To put an antic disposition on

This line in Act 1, Scene 5 marks a major plot development as Hamlet tells Horatio and Marcellus that he is going to pretend to be mad (“put an antic disposition on”) as he plots his revenge on Claudius for murdering his father. This is a puzzling strategy move on Hamlet’s part, to put it mildly, and it opens a series of “Is he really just pretending to be mad or is just mad?” moments that will run throughout the rest of the play. Read more about this quote in Quotes by Theme: Madness versus Cunning (the first quote).