In this soliloquy, spoken immediately after the spirit of Hamlet's father has vanished, Hamlet takes a moment to reflect on what he has just learned. Part of this soliloquy is simply Hamlet's rage and shock at his uncle's treachery and the fact that his mother married such a man. He also resolves to dedicate himself completely to avenging his father's murder:
All saws of books, all forms, all pressures past,
That youth and observation copied there;
And thy commandment all alone shall live
Within the book and volume of my brain,
Unmix'd with baser matter.
One of the more fascinating complexities to this play is that Hamlet is unable to do what he swears to do in this soliloquy. He is distracted, mostly, by his own introspective nature, which causes him to reflect on many of the events that occur around him rather than acting on them immediately. He also commits himself to determining the veracity of the ghost's accusation, which he does with the play.
Finally, Hamlet resolves himself to remember one crucial thing which will serve him well, particularly in his dealings with Guildenstern and Rosencrantz:
That one may smile, and smile, and be a villain;
At least I am sure it may be so in Denmark.