Gertrude betrays Hamlet and the late King Hamlet by marrying Claudius. Hamlet, being still depressed about his father’s death was further upset and felt betrayed by his mother when she quickly married Claudius.
“Mother, you have my father much offended …You are the queen, your husband’s wife …” (3.4.10-15)
By marrying her former husband’s brother, she also betrayed the late King Hamlet.
Another way that Gertrude had betrayed the late King Hamlet was by defending Claudius when he was accused by Laertes of killing his father Polonius:
LAERTES: Where is my father?
QUEEN: But not by him. (4.5.126-128)
Gertrude also betrays Hamlet by telling King Claudius that Hamlet killed Polonius.
Hamlet betrays his father’s ghost by not killing Claudius immediately as he has promised, and how he keeps contemplating over whether or not he should actually kill him.
He also hurts his mother’s feelings, which were against the wishes of the ghost as well.
“Do not forget: this visitation is but to whet thy almost blunted purpose” (3.4.110-111)
Rosencrantz and Guildenstern
Both of these two people were Hamlet’s former schoolmates, and Hamlet entrusted them with the secret that he indeed was not mad. Although they do not betray him at first, they end up agreeing to bring him to death in England.
“[Rosencrantz and Guildenstern’s] grand commission; where I found, Horatio, A royalknavery, an exact command, …That, on the supervise, no leisure bated, No, not to stay the grindling of the axe, My head should be struck off” (5.2.17 – 24).
King Claudius betrays Gertrude by indirectly killing her. He did not tell her that the cup she was going to drink from was poisoned, and he did not stop her either even though he knew.
“It is the poson’d cup; it is too late [for Gertrude]” (5.2.282)
He also betrayed her in the sense that he planned to kill her son that he knew she loved dearly.
“…If he be now return’d…Under the which he shall not choose but fall: And for his death no wind of blame shall breathe, But even his mother shall uncharged the practice, And call it accident.” (4.7.61-67)
Polonius betrays his own son, Laertes by sending a servant to go spy on him:
“You shall do marvellous wisely, good Reynaldo, Before you visit him, to make inquire of his behaviour” (2.2.3-4).
He betrays Laertes’ belief in his trust when he is in France.