Haste me to know 't, that I, with wings as swift as meditation or the thoughts of love, may sweep to my revenge.
Hamlet - Act 2 Scene 2
...What a piece of work is a man! How noble in reason, how infinite in faculty! ... The paragon of animals. And yet, to me, what is this quintessence of dust? Man delights not me. No, nor women neither, though by your smiling you seem to say so.
Hamlet - Act 3 Scene 1
To be, or not to be? That is the question - Whether 'tis nobler in the mind to suffer the slings and arrows of outrageous fortune, or to take arms against a sea of troubles, and, by opposing, end them? ...
This scene in act one is important to Hamlet's character because it sets up what he plans to do for the entire rest of the play. This moment is what starts Hamlet's revenge plot against Claudius. It shows how loyal Hamlet is to his father and how dedicated he is to avenging his father's death.
This scene is important to Hamlet's character because it shows his fascination with mankind. It also shows how observant he is towards everything that is going on around him, even if he does seem very aloof sometimes. Although he is observant he really does not care about other people's lives.
This scene is important to Hamlet's character because it shows that he is contemplating whether it would be better to live or die. He is having an existential crisis and questioning death and what it entails. This all happens because of the chaos going on in his life which causes him to question what the meaning of life is.