My Take on Hamlet
Hamlet is affected by his father's death, he dislikes Claudius, the current king, as he takes King Hamlet's death lightly and also because he marries the widow of his brother very soon after he died. His dislike for Claudius is justified later, when we find out that Claudius murdered Hamlet's father.
After the ghost appeared to him, Hamlet pretended he was mad and used a play to find out if Claudius really murdered King Hamlet. This shows two qualities in Hamlet: he wants to find the truth instead of just "searching his feelings" and coming to conclusions, and he is clever enough to make sure Claudius is not suspicious of his spying.
Hamlet disapproved deeply of his mother's marriage to Claudius, and he tells her this when he meets her in her room. This shows Hamlet's sense of justice, but perhaps he was too rough on his mother, who undoubtedly had reasons for marrying Claudius and did not know of the murder.
In the end, Hamlet kills... a lot of people. Rosencrantz and Guildenstern, Laertes, and Claudius all get tricked or stabbed by our main character. Almost all of these deaths were for REVENGE. Rosencrantz and Guildenstern plotted against Hamlet and were sent to their deaths by Hamlet's forgery. Claudius was taken out for his murder of King Hamlet.
My take on Hamlet's actions is that he set himself up, that the only possible way to get revenge on his uncle was to kill him. If he hadn't feigned his madness, he could have been able to expose his uncle's underhand doings.