King Claudius, the antagonist of Shakespeare's Hamlet, is brother to the deceased King Hamlet, second husband to Gertrude and uncle to the younger Hamlet. He ascends to the throne of Denmark by poisoning his own brother and seducing his brother's widow. He is loosely based on the treacherous chieftain Feng who appears in Chronicon Lethrense and in Saxo Grammaticus' Gesta Danorum. 
Claudius first appears in Act I, scene ii, where he addresses his court, informing them that Young Fortinbras, "holding a weak supposal of our worth," has demanded the surrender of certain lands that were lost by his father to the late King Hamlet. Claudius reveals that he has responded to this threat by writing to Norway, the uncle of Fortinbras, in hopes of suppressing the prince's warlike ambitions. He dispatches Cornelius and Voltemand as ambassadors to Norway for the same purpose. This seemingly minor action, easily overlooked in the opening lines of the scene, is suggestive of Claudius' modus operandi, revealing a preference for stealth and subterfuge over direct confrontation. This matter handled, Claudius quickly turns his attention to Hamlet. Along with the queen, he gently chastises the prince for the dark cloud that he allows to hang over him, saying:
'Tis sweet and commendable in your nature, Hamlet,
To give these mourning duties to your father,
But you must know your father lost a father,
That father lost, lost his, and the survivor bound
In filial obligation for some term
To do obsequious sorrow. But to persevere
In obstinate condolement is a course
Of impious stubbornness. 'Tis unmanly grief.
He goes on to say:
We pray you throw to earth
This unprevailing woe, and think of us
As of a father, for let the world take note,
You are the most immediate to our throne,
And with no less nobility of love
Than that which dearest father bears his son
Do I impart toward you.
Furthermore, Claudius chooses to deny Hamlet's request to return to school at Wittenberg, expressing a desire rather that the prince remain in Elsinore, "Here in the cheer and comfort of our eye." Hamlet reluctantly consents, and were the play to end here, one might think nothing worse of Claudius than that he has been perhaps indiscreet in his hasty marriage to his deceased brother's wife or overly protective of his mourning nephew. But the play does not end here, and a few scenes later (Act I, scene v), we learn the usurper's dark secret. The ghost of Hamlet's father appears to him on the ramparts of the castle, revealing that he has been most foully murdered and that:
The serpent that did sting thy father's life
Now wears his crown.
Hamlet is not shocked by this revelation. On the contrary, he exclaims:
O my prophetic soul! My uncle!
The prince, it seems, is already aware (at least on some some level) of his uncle's true nature. He listens in horror as the ghost recounts the details of Claudius' hideous crime, explaining how he crept into King Hamlet's orchard and while he slept poured into his ear juice of hebenon which:
with a sudden vigour doth posset
And curd, like eager droppings into milk,
The thin and wholesome blood.
The ghost, having known Claudius longer and better than any other character in the play, describes him as "that incestuous, that adulterate beast" who "with witchcraft of his wit" and "with traitorous gifts" seduced the queen. In each case, note that Claudius has chosen trickery and deceit to achieve his aims, murdering the king secretly in his sleep and quietly seducing the queen rather than making a power play for the throne. The ghost, of course, charges Hamlet to avenge his "foul and most unnatural murder," and the stage is set for the action of the play: Hamlet the avenger vs. Claudius the murderer.
The opponents hardly seem equally matched. Claudius is an experienced politician, ruthless and cunning, familiar with the employment of treachery, and Hamlet is an untried youth. While the prince was away at school, passing carefree days with the likes of Rosencrantz and Guildenstern, two foolish youths who expend their limited cunning in the forging of crude witticisms (i.e. residing in the private parts of Fortune), Claudius was diligently plotting his rise to power, laying the groundwork for the clandestine assassination of King Hamlet, a coup he pulls off without anyone (other than Hamlet apparently) even suspecting foul play. In fact, he has the old king's courtiers, groveling bootlickers like Polonius, eating out of his hand. A master manipulator, Claudius appears to have little fear of Hamlet, his brooding nephew who seems only moderately successful even in the diversions of youth -- his love suit to Ophelia, for instance, which is so easily undermined by her father. In addition, Claudius has the entire court at his disposal, while Hamlet trusts no one, not even his closest friend, Horatio, from whom he hides the facts of his uncle's transgression until the play scene (Act III, scene ii) when he finally enlists his friend's aid in determining the king's guilt. By all outward appearances, Claudius would seem to hold the advantage in the game of cat and mouse that is about to ensue. He only seems to be sharpening his claws. But appearances can be deceiving, and as one critic writes, Claudius' confident display of kingly power is perhaps more air than substance:
Claudius is, from one point of view, another Player King: a "thing of shreds and patches", as Hamlet calls him, referring to the motley of the "Vice" or clown.... Claudius is an example of a spurious kind of authority, who has the persuasiveness and physical courage of a ruler, but who is morally empty. 
Not all critics, however, are prepared to accept Claudius as an empty suit. In fact, some have even taken the remarkable position of becoming apologists for the usurper, suggesting that, regardless of his method of ascension, Claudius would have made a fine king and that Denmark would have been better off under his rule, describing him as "calm, reasonable, decisive,"  pointing out that:
Denmark is a healthy and contented community with Claudius as its efficient and kindly administrator, sensibly not wishing to let memories of the past impede the promise of the future. 
and even writing:
Claudius, as he appears in the play, is not a criminal. He is -- strange as it may seem -- a good and gentle king, enmeshed by the chain of causality linking him with his crime. And this chain he might, perhaps, have broken except for Hamlet, and all would have been well. 
This sort of specious argument seems like the kind of contorted logic that one might expect from the mouth of the usurper himself, or else one of his sycophants. It is a brittle defense, to say the least, and crumbles during the play scene when Claudius' mask of competence is so easily shattered by the presentation of Hamlet's play. Would such an able king as these critics describe allow himself to be visibly rattled by a theatrical reenactment of his crime? Would he rush from the theatre calling for light, as Claudius does, or would he calmly sit through the entertainment, revealing nothing, smiling, even applauding perhaps? The presentation of the play is little more than a school boy's trick, and yet it is sufficient to reveal Claudius' "calm, reasonable, decisive" exterior as a thin facade, an illusion whose magic is easily dispelled by a discerning eye. If the rest of the court were not bewitched by Claudius' spell, they too would see what Hamlet and Horatio observe -- a criminal exposed.
Have there been earlier signs of his weak and depraved nature? From the very beginning of the play, Claudius is perhaps overly eager to know the cause of Hamlet's brooding. While Gertrude is more concerned with Hamlet's well-being, her husband's interest seems to revolve around finding the hidden cause of Hamlet's unnatural temperament. (Perhaps because he suspects the truth!) He is vexed at the prince's refusal to accept the natural course of life and to move on (as the rest of the court has done, including Gertrude). In retrospect this is probably a sign of fear, an inability to manage his own guilty conscience. Claudius is not a cool manipulator like Iago. Neither is he the bold decision maker that some critics make him out to be. Whenever he is ready to take decisive action, he allows himself to be dissuaded by others. When he first decides to send Hamlet away, for instance, he listens to the counsel of Polonius and is led astray, persuaded to explore the possibility that Hamlet's brooding is merely a product of his infatuation with Ophelia (when all of his instincts scream that it is not).
It is probable that Claudius' suffers from feelings of inadequacey after living most of his life in the shadow of his more able brother. As Hamlet makes clear in the interview with his mother (Act III, scene iv), there is an enormous gap between the two men:
Look here, upon this picture, and on this,
The counterfeit presentment of two brothers.
See what a grace was seated on this brow:
Hyperion's curls, the front of Jove himself,
An eye like Mars, to threaten and command,
A station like the herald Mercury
New lighted on a heaven-kissing hill;
A combination and a form indeed
Where every god did seem to set his seal
To give the world assurance of a man.
This was your husband. Look you now what follows.
Here is your husband, like a mildewed ear,
Blasting his wholesome brother. Have you eyes?
Could you on this fair mountain leave to feed
And batten on this moor?
If there is any truth to Hamlet's words, how Claudius must have cringed at any comparison to his brother -- how he must have feared his shortcomings would be exposed by the juxtaposition of their contrasting natures.
After his meltdown during the play scene, Claudius makes a weak attempt at repentance, retreating to his chambers to pray, but finds that he is unable.
O, what form of prayer
Can serve my turn? 'Forgive me my foul murder'?
That cannot be, since I am still possessed
Of those effects for which I did the murder,
My crown, mine own ambition and my queen.
May one be pardoned and retain the offense? (Act III, scene iii)
Though he forces himself to pray ("Bow, stubborn knees!"), Claudius does not in his heart repent. Unwilling to relinquish the fruits of his crime, he plunges ahead instead with his wickedness. How lost he is, how deeply immersed in darkness, becomes clear in his Machiavellian subversion of Laertes (Act IV, scene v and vii).
Violent, self-willed, irrational, Laertes is easily maneuvered into a seemingly foolproof plot against Hamlet's life. Emblematic of purpose, passion, and memory at their worst, Laertes will stick at nothing to live up to his own warped conception of honor. 
But Claudius' trickery is too indirect. He holds all the power, yet he fears direct confrontation. He could easily have the prince slain but he fears the reaction of the people and of his queen. Instead, he recruits multiple partners to carry out this treachery in secret -- Laertes, Rosencrantz and Guildenstern, the king of England -- but these plots fail, being too elaborate and long-winded. The young inexperienced prince outwits Claudius and his minions at every turn because (in spite of his reputation as a man incapable of action and unlike his uncle who better deserves such renown) Hamlet recognizes opportunity when it presents itself and seizes it boldly and directly. Claudius could learn from his nephew, but he does not. In the end, he falls victim to his own (too elaborate) scheme, run through with the poisoned blade he intended for Hamlet. He is undone by his own weakness. Enslaved by ambition and driven to acts of immorality and lawlessness by his sexual appetite and his lust for power, Claudius is ultimately undone by a lack of fortitude, a lack of commitment to his own evil nature and a need to be seen as honorable when he is not.
- Looking for Hamlet. Marvin W. Hunt. New York: Palgrave Macmillan, 2007.
- The Ghost of Hamlet: The Play and Modern Writers. Martin Scofield. Cambridge: Cambridge University Press, 1980.
- Hamlet in Pieces. Andy Lavender. London: Nick Hern Books, 2001.
- Hamlet Prince of Denmark. Ed. Brian Gibbons. Cambridge: Cambridge University Press, 2012.
- The Wheel of Fire. George Wilson Knight. Oxford: Oxford University Press, 1930.
- Hamlet's Search for Meaning. Walter N. King. Athens: University of George Press, 1982.