How do Hamlet, Polonius, and Claudius use disguise to subvert their true natures and purposes and thereby achieve power? My main topic here is "Appearance Vs. Reality."
The themes of disguise and "appearance vs. reality" are central to the play; namely in that certain characters "act" differently in order to fool others. Claudius, Hamlet, and Polonius use disguise as a means to achieve some end, and you could argue that the "end" is power for each.
Claudius appears or disguises himself as the new, dutiful king, loyal to the legacy of his brother and genuinely in love with Gertrude. This "act" or disguise is a mask for what he really is: a murderer who pretends to be the dutiful king in order to achieve the power of being king. Claudius is acutely aware of his duplicity. Note in Act 3, Scene 3, the scene ends with Claudius saying, "My words fly up, my thoughts remain below: / Words without thoughts never to heaven go." Claudius appears to be in a penitent, sacred state; so, Hamlet decides not to kill him yet. This was fortunate, temporarily for Claudius, but in general, he tries to appear this way, except when the audience hears his dialogues with Polonius and Laertes in trying to secure his power from Hamlet.
Hamlet's entire strategy is about deception and disguise. Although Polonius is often mistaken about things, he rightly points out that Hamlet's madness is a disguise for some other purpose. "Though this be madness, yet / there is a method in't." (II.ii.216-17) Hamlet's use of appearing melancholy, then mad is all a means to keep others guessing and unsure about what Hamlet is up to.
Polonius appears to befriend Hamlet (Act II, Scene 2), but again, his intention is to spy on Hamlet and find out the "method to his madness." Polonius says he has the ability to figure all of this out, but he's often mistaken in his conclusions. His efforts are to appease Claudius and secure his position as a kind of right-hand-man to the king.
Each character "acts" a certain way in order to achieve some position. Claudius acts like a gracious king in order to be the king: for power. He also acts like a friend to Hamlet but that is to protect himself from Hamlet and perhaps get rid of him. Polonius "acts" in different ways, but all for the selfish reasons of being in a high government position with Claudius as leader: a powerful position. Hamlet "acts" mad (crazy) to keep everyone unsure of his method (his plan for revenge): a position that gives him the power and/or space to carry out his revenge.
This is an interesting topic in that it shows how this play is really about "acting." These characters are often "not themselves" in the sense that they are always acting in different ways. This is fitting considering that there is a play within this play ("The Mousetrap"), since the characters also behave like actors utilizing different roles in order to confuse the others.