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Marcellus wants Horatio to speak to the apparition because Horatio is a well educated man who is skeptical of the supernatural. 
Fortinbras, the young Prince of Norway, wants to reconquer the land he lost to the King. 
The soldiers/guards want to tell Prince Hamlet. 
The King tells Prince Hamlet to stop whining/being openly depressed about his father because it’s not manly. This, as I astutely pointed out in class, is very similar Malcolm’s conversation with Macduff. 
Prince Hamlet is upset because of his father’s death and his Uncle’s untimely assumption of his fallen father’s role. 
Laertes tells Ophelia to be circumspect about falling in love with Hamlet. 
Polonius tells Laertes to be punctilious and mindful of who he spends his time with. 
Ophelia agrees to “obey” both Polonius and Laertes’ advice to dissociate herself with Prince Hamlet. 
The ghost claims to be Hamlet’s father’s spirit and the ghost tells him that his father was murdered. The ghost also tells Hamlet how his father was murdered and by whom. Finally, the ghost tells Hamlet to enact revenge. 
 Prince Hamlet makes him swear that he does not mention what he saw to anyone. Prince Hamlet also makes him swear not to reveal his own true reasons for his actions as he may pretend to act crazy.