Act I, scene II opens with King Hamlet's (Hamlet's father's) recent death still casting its shadow over the court. Claudius, the new king, immediately states
Though yet of Hamlet our dear brother’s deathThe memory be green ...
A little more than kin and less than kind.
At the beginning of Act I, Scene 2 of Hamlet, Claudius approaches court life with a happy and businesslike tone. Dismissing the recent death of his brother, he says it's time to move on, or, in his words, "we with wisest sorrow think on him/ Together with remembrance of ourselves" (lines 6-7). In other words, Claudius says it's time to think about himself, so he has chosen to marry his brother's widow, Gertrude.
Claudius quickly moves to conducting business in a way that seems callous, given his brother's recent death. He decides to tell Fortinbras that his plans to recover the lands his father lost to the deceased King Hamlet are not to come to pass, and Claudius dispatches Voltemand and Cornelius to tell Fortinbras this news. Claudius then moves to hear Laertes's request that he return to France and grants it. The mood of the court is so brisk and upbeat that Claudius lectures Hamlet, "How is it that the clouds still hang on you?" (line 66). In other words, even though Hamlet's father has recently died, Claudius is surprised that Hamlet is still in mourning. He urges Hamlet to stop mourning and move on.
The atmosphere is unsettled at best. Claudius begins with the "happy" announcement of his marriage to Gertrude, praising her beauty and celebrating his position as king. He speaks lavishly of his love of his wife and his people, including Hamlet. But then he immediately launches into his concern that Fortinbras will challenge Denmark in war. At the same time, Hamlet is moping off to the side, making snide comments to himself and responding with bitter remarks to the loving comments of his uncle and mother. The audience is left to feel that this is a country - and a family - in turmoil.