In Shakespeare's Hamlet, we see two different sides to the Prince of Denmark.
First, we see him as a devoted son who is devastated by his mother's seemingly hasty marriage to her brother-in-law, Claudius (Hamlet's uncle.)
My lord, I came to see your father's funeral.
I prithee do not mock me, fellow student.
I think it was to see my mother's wedding.
Indeed, my lord, it followed hard upon.
Thrift, thrift, Horatio. The funeral baked meats
Did coldly furnish forth the marriage tables. (I.ii.181-186)
Hamlet tells Horatio that while his friend came for Old Hamlet's funeral, the ensuing marriage took place so swiftly that they used the leftovers from the funeral for the wedding feast. (This is exaggeration, or hyperbole.) All of this infers Hamlet's devotion to his father and disappointment in his mother's actions.
When Hamlet learns that his father has been murdered by his uncle, he is charged by the ghost of his dead father to exact revenge for Old Hamlet's death. And although Hamlet wants to do so, he is fearful in case the ghost is really the devil appearing to look like his dead father. For if Hamlet kills a king wrongfully, he would lose his soul to eternal damnation. It is at this point that we see the other side of Hamlet: the angry vengeful man who becomes suspicious of Ophelia and ruthless with Gertrude, his mother. In order to move about the castle without seeming to be a threat to the King and his supporters, Hamlet pretends to be insane. He warns Horatio of his plan.
As I perchance hereafter shall think meet
To put an antic disposition on—
That you, at such times seeing me, never shall... (I.v.191-193)
That you know aught of me... (198-199)
In Act Three, Hamlet tells Ophelia that he never loved her and that she should join a convent. He tries to convince her that he is a horrible person, but he's lying because he believes she is spying on him, to report what she learns to her father, Polonius, and King Claudius.
Get thee to a nunnery! Why wouldst thou be a
breeder of sinners? I am myself indifferent honest, but yet
I could accuse me of such things that it were better my
mother had not borne me. I am very proud, revengeful,
ambitious; with more offences at my beck than I have
thoughts to put them in, imagination to give them shape,
or time to act them in. (III.i.133-136)
By the next scene, Hamlet has hired some traveling players to act out the murder of his father in a play they are performing. He hopes in doing so to "catch the conscience of the King," Claudius (II.ii.605).
He poisons him i' the garden for his estate. His name's
Gonzago. The story is extant, and written in very choice
Italian. You shall see anon how the murderer gets the love of
Gonzago's wife. (III.ii.250-253)
Seeing the similarities between the play and what he has done, Claudius withdraws suddenly from the theatrical performance, convincing Hamlet by these actions that he (Claudius) is guilty of murder, as the Ghost had said in the first act. Hamlet now has his proof.
Here, then, are two very different sides of Hamlet: the loving son and the avenging "angel." He is the friend of Horatio who had little to worry about while at school, who now carries the weight of the world upon his shoulders as he tries to make right the terrible wrong his uncle has done.
Hamlet can be seen by some as harmless, but in truth his other side shows that he is clever and determined.