This is Claudius' first "set" speech; he looks good, explains the quickness of the marriage while the country was supposedly still in mourning, handles the major problem was hinted at scene 1, takes care of Laertes well, and finally turns to a problem within the royal family. His language is masterly. His oxymorons such as "defeated joy", "mirth in funeral and dirge in marriage" allow the audience to focus in on whatever emotion they want to find. Those who are still mourning will hear "defeated", "funeral", and "dirge"; those who are celebrating the wedding will hear "joy", "mirth", and "marriage." The language is appropriate for the formal, ritualistic situation.
In successful Machiavellian manner, Claudius has figured out a way to handle the threat of Fortinbras at the cheapest possible cost.
Claudius flatters Laertes by using his name often, using his first name which suggests a more informal relationship with Laertes and Polonius. During this speech, Claudius calls himself "The Dane" as the King
Hamlet's language, like his costume, is strikingly different from the formal, ritualistic quality of the King's speech; here, Hamlet is cynical, sarcastic. His pun suggest that he is closer in kin to Claudius than he would like to be, yet he does not believe Claudius feels kindly towards him. Notice that the pun would have worked as well if, instead of "kind" Hamlet had said "king." He is still the Prince, not the King as he perhaps should have been through the law of primogeniture as the son of the Old King.
Hamlet acknowledges that his appearance could be faked, but his use of the "inky cloak" truly denotes his inner feelings, and he would certainly not fake anything. He is claiming to be the True in a world of Counterfeits. This suggests that Hamlet believes that appearance and reality are one and the same; later after seeing the ghost, he changes his mind and acknowledges that "a man may smile and smile and be a villain." But it comes to him as a revelation or epiphany when his suspicion of Claudius' villany is confirmed by the ghost. This first view point is closer to the Renaissance Christian Humanist than the Machiavellian. The view that a man may smile and be a villain is more of a Machiavellian view.
Claudius tries to sound friendly but is very critical of Hamlet, here suggesting that his grief makes him unmanly. Claudius lectures Hamlet, saying about the same thing that Gertrude did, but suggesting that Hamlet's actions are against heaven. Of course, when we realize that Claudius killed Old Hamlet, this speech in retrospect is the ultimate in hypocracy. In scenes 2,3, and 5 of this act, fathers (or in this case a step-father) lecture to their children, telling them what to do.
Again, in a smart Machiavellian move, Claudius tries to forestall Hamlet's potential ambition to be King, which might find supporters among the court or the people, by announcing that Hamlet is his heir. In Denmark the succession to the throne is decided by the court, not the way England would use, the oldest son inheriting the crown. However, this would be an issue to the Elizabethan audience who was very concerned about whether there might be civil war after her death if she did not have an heir or clearly name her successor.
Hamlet acknowledges Gertrude's position in his family as deserving of duty, but ignores Claudius. But Claudius, being the smart manipulator, can turn this answer into a good way to "win" in front of the court. He quickly leaves the stage before this impression can change.
Hamlet gives us the first view of death, that it would be relief to one who is deep into grief. But he also verbalizes the view that suicide is a sin. He sees the world as a declining world, going from the ideal of the past when his father was King to the corruption of the court by Claudius.
Memory brings the past into his awareness and makes him sad because it seems so much worse. How one is remembered and for how long after his death is a theme that Hamlet wrestles with throughout the the play.
Hamlet is as upset about his mother's remarriage as he is about his father's death. His mother's willingness to marry Claudius undercuts Hamlet's view that his mother and father loved each other deeply.
This is an ironical statement; Hercules accomplishes 12 mighty labors, yet Hamlet cannot even perform one task given him by the ghost. Hamlet is also suggesting that he himself is part of this declining world; he is cynical even about himself.
Hamlet tests everyone. He wonders how Horatio might have heard that first speech of Claudius'; is he still grieving for the dead king or celebrating the marriage of the queen.
Again Hamlet tests Horatio. Here he tries to use a falsehood to reveal that Horatio's tale of seeing a ghost of his father was just made up, but Horatio corrects him.
This world view is a remnant of the Renaissance Christian Humanist view that God has a plan and he will revenge all wrongs, bring to light wrong-doings. Here Hamlet is willing to wait on God's timing to reveal why things are so rotten in Denmark.