Polonius is sure, at first, that Hamlet would never marry Ophelia, because of the difference in social status, so he thinks that Hamlet must be only trifling with Ophelia, just for sex. Polonius fears Hamlet doesn't really love Ophelia, and he would get Ophelia pregnant, and then abandon her. We see that in Act 1 scene 3. (Later, in Act 2 scene 1, Polonius changes his mind, however.)
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Polonius advises Ophelia to avoid Hamlet because he believes that it was not true love for which Hamlet loved her for. Thus, Polonius believes that once Hamlet becomes King, he would end up marrying someone else.
Hamlet, being the son of the Queen and the heir apparent to the throne, was not in a position to marry whoever he wanted. Any marriage of such a person was a political act, and needed the approval of the court. Polonius thinks that Hamlet is just trying to get into Ophelia's pants and doesn't want her to compromise her reputation by going too far with him.
It is sad to know that the Queen would have gladly approved such a marriage, and indeed would have encouraged it, but we only hear this at Ophelia's funeral. "I hoped thou shouldst have been my Hamlet's wife."
Laertes instructs Ophelia to stay away from Hamlet because he believes that Hamlet will not be able to marry Ophelia even if he really does love her.
to be a romeo in real life and stay with his Juliet in a hamlet.
They both say they want Hamlet to stay at Elsinore Castle instead of going back to school at Wittenberg.
Well, I must first of all say that my statement is of my own interpretation of the story. However, it may be possible that Claudius was planning on killing off Hamlet (or at least spy on him) from the very beginning. By looking at Claudius's personality, namely his willingness to kill for power, it can be implied that Claudius is fearful of loosing his power in the same way. Of all that may pose a threat to Claudius, Hamlet seems to be the most likely threat as he is in direct line to the throne (after all why not kill off the king and become the new king a little ahead of schedule?). So due to Claudius's paranoid nature, it may be possible that he intended to keep Hamlet in Elsinore so that he could plot to get rid of him.
Dirkinshnof Toejam. he was from canada :)