Hamlet Act 3

S1: Rosencrantz and Guildenstern Report to the king on Hamlet.
~ Ophelia goes in a plot with her father and king to return Hamlet's letters -> Hamlet see through the act and confesses to Ophilea he never loved her and tells her to get to a nunnery.
~Polonius and Claudius conclude to send Hamlet away after his mother questions him one last time.

S2: Hamlet coaches the actors.
~ The play runs.
-> The King runs out after the talk of poising the player king.
~ Guildenstern strives to confide in Hamlet once more. Hamlet rebukes Guildenstern and tells him that his shall not play him like a pipe.
~> One gets the sense that things are not always as they appear, that people play many roles as they go through life. One must be careful of the motives of other.

S3: The faculties of Ambition
~ Claudius remorses to himself seeks repentance with no avail for he cannot bring himself to give up the rewards of his evil--his wife and kingdom.
~Hamlet finds him praying, finally "resolved" to kill him, yet decides he will wait till Claudius is not clean and ready to meet his maker.

S4: Hamlet confronts his mother.
~Polonius spy on the affair and cries out in a moment of disarray and is killed by hamlet.
~Hamlet was hoping it was Claudius behind the curtain.

One of the points that I thought was interesting is when Hamlet is speaking to the players before the play. He tells them not to overdo the act:

I had as live the town crier spoke my lines. Nor do 1885
not saw the air too much with your hand, thus, but use all
gently; for in the very torrent, tempest, and (as I may say)
whirlwind of your passion, you must acquire and beget a
temperance that may give it smoothness. O, it offends me to the
soul to hear a robustious periwig-pated fellow tear a passion to 1890
tatters, to very rags, to split the cars of the groundlings, who
(for the most part) are capable of nothing but inexplicable dumb
shows and noise. I would have such a fellow whipp'd for o'erdoing
Termagant. It out-herods Herod. Pray you avoid it.

Be not too tame neither; but let your own discretion be your
tutor. Suit the action to the word, the word to the action; with
this special observance, that you o'erstep not the modesty of
nature: for anything so overdone is from the purpose of playing,
whose end, both at the first and now, was and is, to hold, as 1900
'twere, the mirror up to nature; to show Virtue her own feature,
scorn her own image, and the very age and body of the time his
form and pressure. Now this overdone, or come tardy off, though
it make the unskilful laugh, cannot but make the judicious
grieve; the censure of the which one must in your allowance 1905
o'erweigh a whole theatre of others. O, there be players that I
have seen play, and heard others praise, and that highly (not to
speak it profanely), that, neither having the accent of
Christians, nor the gait of Christian, pagan, nor man, have so
strutted and bellowed that I have thought some of Nature's 1910
journeymen had made men, and not made them well, they imitated
humanity so abominably.

He tells them to let nature act as nature, if one is to act virtue, passion, anger, or norm let them look as such. And later in the play he speaks with Horatio and commends him for not being passions slave.

and blest are those
Whose blood and judgment are so well commingled
That they are not a pipe for Fortune's finger
To sound what stop she please. Give me that man 1950
That is not passion's slave, and I will wear him
In my heart's core, ay, in my heart of heart,
As I do thee.

It is interesting that in these two passages he is commending the idea of restraint and patience, yet he is quickly becoming the unbridled passion he is counseling against. In a moment to avenge his father’s death--seeing the king praying alone in his room--hemlet decides to postpone his action yet again. This time however not for uncertainty but because he thinks the king will ironically go to Heaven if killed while praying. Hamlet in passion and revenge and hate now chooses to wait for a time when he thinks Claudius will be ripe to go to hell and suffer the most. He wants Claudius to pay for what he has done. This growing passion leads to Polonius's death while spying in the queens chamber, upon a cry Hamlet hopes it to be his 'father' and stabs blindly into the drapes killing him.

There is a lesson here on passion and ambition. Claudius's ambition leads to the death Hamlet's father the true king. Hamlet's passion has led to the death of Polonius. Both have killed in the name of passion and ambition. Who’s to say now they both don't deserve the same fate? Unbridled passion and ambition is not a good thing!
One more thought: Hamlet calls the play to expose Claudius's evil 'Mouse Trap’. Hamlet as compels his mother not to fall for Claudius's evil seductions any more saying 'Not this, by no means, that I bid you do:
Let the bloat King tempt you again to bed;
Pinch wanton on your cheek; call you his mouse;'
In both place when there is one leading the other into one's will they are referred to as mouse. Hamlet is playing with the king and the king with Gertrude.