Revenge
One of the first key plot moments starts with Hamlet talking to The Ghost, his deceased father, Old King Hamlet. The Ghost claims that his brother, the new King Claudius had poisoned and killed him in order to become king. Old King Hamlet tells his son that he wants revenge and wants his son, Prince Hamlet, to kill him. Instead of executing his uncle immediately, he decides to wait. If he were to wait and pretend to act crazy, he would not pose as a big threat for Claudius's murder as opposed to killing him as soon as he was told. Revenge to Hamlet, becomes a first and only priority throughout the entire play.
Deceit
There's no doubt that Hamlet hates lying, especially when it comes form his uncle, King Claudius. Despite his hatred for deceit, Hamlet actually misleads his family and friends to believe that he has gone insane. Doing so, he can deceive the public to conclude that he is no hazard to the king and thus, kill him without getting into much trouble. Whilst Hamlet pretends to be crazy, King Claudius makes a plan of his own, having people spy on Hamlet and attempts to poison him during the duel with a contaminated drink and sword. Deceit is absolutely necessary for Hamlet and evolves into his main motivation to kill his uncle successfully.
Relationships
In Hamlet, relationships are constantly stressed, whether it be a family or friend relationship or one with a lover. Essentially, this is shown most often regarding Hamlet's feelings toward the marriage of his mother and uncle. When he does talk to his mother, he normally is making a rude remark, calling it incest or reminding her about his father. Likewise, when ever he talks to his uncle, Hamlet becomes witty with his responses, calling him mother and hinting at the fact that Claudius killed his own brother.
Mortality and Suicide
In the beginning of the play, Hamlet constantly talks about wanting to kill himself. His suicidal tendencies began after his fathers death and when his mom, the Queen, married his uncle, Claudius two months after his father passed away. It seemed to him that nobody cared about his father besides him, with his own mother telling him, in other words, to get over it. Once he met with The Ghost, he decided that he finally had some sort of purpose to be alive, even if it was to kill someone as where before he felt life was only full of pain and death.
Turning Tables
The theme of turning tables or exchange in situation goes hand in hand with revenge. However, the main difference is that the reversed situation is self-inflicted rather than revenge where it seen as a "eye for an eye." For example, Claudius killed his own brother in order to marry the queen and become king himself. In the end, during Hamlet's play, he felt so guilty and uncomfortable that he left to go pray. Additionally, this is shown when Laertes and Hamlet duel each other. As they both realize that they will die soon, Laertes apologizes and tells him the King's plan out of guilt.