What are examples of the many plots and schemes in Hamlet, and how would you describe those devised by Hamlet?

It seems that, more than any other Shakespeare play,
Hamlet is renowned for its many plots hatched by many characters
and sucking everybody in to them, whether they like it or not or are aware of how they
are being used. Of course, the plots that other characters devise are mainly hatched by
Claudius and Polonius to try and establish what is the cause of Hamlet's "antic
disposition." Thus they enlist Ophelia, eavesdropping on her conversation with Hamlet in
Act III scene 1, and also Gertrude after the play in Act III scene 4. In addition,
Claudius turns Hamlet's friends against him, asking Rosencrantz and Guildenstern to help
discern what ails the young prince. Plots surround Hamlet left, right and centre, and we
can't help but feel sorry for him as those who should be closest to him are turned
against him.

However, at the same time, Hamlet shows that
he is no novice himself in the art of plots and stratagems. It is he who tests out the
words of the Ghost by creating The Mousetrap as an elaborate trap to "catch the
conscience of the King," and he is able to effectively detect the betrayal of both
Rosencrantz and Guildenstern and Ophelia. Note the way he plots his revenge against his
former friends by having them executed. If Hamlet is sinned against, he shows himself to
be equally sinning in this regard, responding with plots and stratagems of his own that
are arguably more successful than those of other characters. After all, he gets the
reaction that he had wanted from Claudius during his play, and he is successful in
disposing of Rosencrantz and Guildenstern.