"That, if again this apparition come, He may approve our eyes and speak to it."(I.i.33)
"Within a month, Ere yet the salt of most unrighteous sheets tears Had left the flushing in her galled eyes, She married."(I.ii.168-161)
The Play begins with the guardsmen reporting of a ghost sighting and Horatio reporting the news of Fortinbras preparing to invade Danmark to get back the land Hamlet's father took from Fortinbras' uncle. This foreshadows key events in the play including when Hamlet would see his father, the ghost, and completely alter his future with the need for revenge.
Hamlet's first soliloquy, in which he is in morning of his father's death. Its only been a month since then and his mother has married an awful man, his uncle Claudius. This development means shes committing incest with her brother-in-law make Hamlet even more upset, to the point that he questions the possibility of suicide. Hamlet's mental stability is very low at the start of the play.
The play begins to escalate when Hamlet meets the Ghost that Horatio and others have already seen. Although at first in disbelief, Hamlet soon realizes that it must be his father's ghost, for he recognizes the armor that the Ghost is wearing. Hamlets attitude shifts from sullen to revengeful when he hears of the murderer of his father has both the throne and his mother.
"O, from this time forth My thoughts be bloody or be nothing worth!"(IV.v.68-69)
Hamlet is lying in wait for Claudius to react to the play, and the actions of the players. Specifically, the action of murder by Lucianus against the Player King. With the confirmation of Claudius' murder, Hamlet now has nothing to stop him from exacting his revenge. Except he doesn't, the morals of murder and the events that occur after death hold him back. Hamlet needs a few more acts to continue changing, at least until he reaces the point of following through.
"Give me some light. Away!"(III.ii.295)
Hamlet stabs into a mouse, a body, a Polonius, unknowingly but the outcome of the event will affect his manor. The murder of Polonius has no direct effect on Hamlet, he shows no remorse. Hamlet though showed a shift in attitude towards his mother's actions. He begins to berate her for marrying Claudius so soon after her husband's death. This means Hamlet is more willing to cross lines that shouldn't be crossed, like calling your mother a slut.
After seeing Fortinbras' bravery and thirst for battle, Hamlet begins his soliloquy to give himself a pep talk. Hamlet has spent most of the play mopping about his father's death and his mother's act of incest, as well as planning and talking himself up. This is one of the last pushes before Hamlet takes action against Claudius. It takes Hamlet seeing Fortinbras, a foil to Hamlet, to motivate him to follow suit on those plans.