Politics
How effective is Claudius as ruler? At the beginning of the play he seems to act with despatch: he deals promptly with the threat that Fortinbras poses, and he approaches the domestic requests of Laertes and Hamlet with tact.
His way of dealing with problems tends to the indirect, as his use of poison to kill Hamlet's father while sleeping attests. He follows Polonius' advice in setting up Ophelia to eavesdrop on Hamlet, sends secret orders to the English to kill Hamlet on arrival, and skilfully manipulates Laertes into the plot to eliminate Hamlet.
How much do we know of what Claudius thinks*? Is he, as politician, in part following the precepts of Machiavelli?
Footnotes
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Getting to know Claudius
Compared with some of Shakespeare's villains (Iago or Edmund for example), we know little of Claudius' inner life. It is not until well into the third act that, in an aside, Claudius confirms the accusation of the Ghost, and not until after the play-within-the-play that he has a soliloquy examining his conscience.