Why Does Hamlet Act Crazy?

In the play, Hamlet mourns the death of his father, who had been killed and is frustrated by the behavior of his mother, Gertrude, who married his uncle, Claudius, just months after his father’s passing. Hamlet is visited by the ghost of his father. During the visits, he is told that his father was poisoned by Claudius and that he should avenge his father’s murder. Not yet sure if he believes the ghost, he goes back to the palace pretending to be mad in front of Claudius and the rest of the court. Claudius, skeptical of Hamlet’s behavior, sends Rosencrantz and Guildenstern, old friends of Hamlet, to spy on him. Catching on to what is going on, Hamlet plays mad.
Determined to convince himself to carry out the premeditated murder of his uncle, Hamlet pretends to have fallen into a complete madness hoping that his performance will be strong enough to carry out with the plan. In his new found madness he proceeds to hire actors to perform before the entire castle a slightly altered version of the play, The Mousetrap to ensure Claudius’s guilt: “Before mine uncle, I’ll observe his looks,/I’ll tent him to the quick, if a’ do blench.”. This provides him material proof that the words of his ghostly father are true before he proceeds to attempt to murder Claudius’s life.
Hamlet also uses his girlfriend, Ophelia by acting threatening and insane towards her. He does this because he knows that Ophelia will tell her father, Polonius about Hamlet’s demeanor and the word will eventually reach Claudius. This way, Claudius will not suspect that Hamlet knows about the treason he has committed. Hamlet keeps a facade to hide his true motives by instilling different personas to keep up with his false pretences.
To sum up, Hamlet maintains an illusionary exterior appearance of a mad man to keep others from knowing what he is really planning: the murder of Claudius.