Spying is an one of the many themes in William Shakespeare's “Hamlet” because so many of the characters are involved in it. By far the worst criminal is Polonius. He is the king's right-hand man, so we presume he has had some practice at it. But, he spies even on his own children, by sending Reynaldo, his servant, to spy on his son, Laertes.
Another point is where Polonius and Claudius both spy on Hamlet and Ophelia: “At such a time I'll loose my daughter to him:
Be you and I behind an arras then;
Mark the encounter: if he love her not
And be not from his reason fall'n thereon,
Let me be no assistant for a state,
But keep a farm and carters.”
He rather risks his own life by spying, in one incident. Polonius dies while he is hiding behind the curtains in Gertrude's bedroom, spying again on Hamlet.
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He acts as Hamlet's spy when he watches for Claudius to react on the existence of the ghost. Rosencrantz and Guildenstern are both spies for Claudius and Gertrude, though they are mostly bad at it. Their spying also gets them killed. There is also another part of spying with Fortinbras, as he prepares to fight Denmark and lies to his uncle about it. Even the Ghost appears in Gertrude's bedroom, presumably spying on how things are going between his wife and son. Claudius is the king, and it should be under him to do his spying himself, but he does. Either way Polonius and him both spy on Hamlet and Ophelia. Claudius also asks Hamlet's friends Rosencrantz and Guildenstern to spy on Hamlet, and, by the way, Gertrude consents to both of these spying episodes on her own