* Permission to return to France: He's been studying abroad in France and initially wants to go back.
* Revenge for his father's death: After discovering that his father, Polonius, was murdered by Hamlet, Laertes demands justice and seeks permission from Claudius to avenge his father's death.
* To be made "the first man" in Denmark: Laertes implies that he is more worthy of being the king's favorite than Hamlet. He wants to be given a position of power and authority.
Laertes's demands are fueled by a mixture of grief, ambition, and a desire to prove himself. He is also manipulated by Claudius, who subtly encourages Laertes to take revenge on Hamlet, further complicating the already turbulent situation in Denmark.