Prince Hamlet is the son of the recently deceased King Hamlet. Although the Prince was in line for the throne at the time of his father's death, the Danes apparently had some type of electoral process and Claudius was able to persuade the body to elect him. I think we see more than a few traces of resentment in the Prince, but he never directly complains at length or cries out, "I should be the King!" ...

Ophelia is the young woman at court (Polonius' daughter; Laertes' sister) with whom Hamlet has shown a romantic interest. We get only references to their relationship. Letters and perhaps love tokens were exchanged. Was there anything more? Hard to say, but many directors of the play have assumed so. Polonius clearly is worried that Ophelia may allow an inappropriate level of intimacy with Hamlet ...

Gertrude is Hamlet's mother. She is somewhat aloof as would befit a queen, but she is fairly warm in her approach to Hamlet in the early acts. She married Claudius shortly after her husband, King Hamlet died. At court there seems to be no suspicion surrounding King Hamlet's sudden and untimely death. But does Gertrude know her husband was murdered? Does she know who did it? Was she a co-conspirator? ...

Claudius is also an unknown character. We only get a close look at him when he is praying and asking for forgiveness. He does not seem a particularly powerful man. He kills his brother when he is sleeping-- not exactly a courageous act. Clearly events are slipping away from Claudius in the course of the play. I do not understand why he does not send Hamlet back to school as he requests at the beginning of the play...