Richard III generated a great deal of interest both during and after Shakespeare's lifetime. It was published in quarto at least five times after being performed in 1592. Richard Burbage first played Richard the Third and made the "poisonous bunchbacked toad" (1.3.244) into one of the most memorable villains of all time.
Another play, The True Tragedy of Richard III, which was also published around the same time, failed to have as compelling a Richard III. Richard's portrayal as an evil villain lent credence to what historians call the "Tudor Myth." The Tudor dynasty was founded when Henry, Earl of Richmond, defeated Richard III at the Battle of Bosworth Field in 1485. Henry assumed the throne as Henry VII, and was grandfather to Queen Elizabeth I. Having won the throne in battle, it was essential for the Tudor's to discredit older claims. Thus they depicted Richard III, who was the last Yorkist king, in as terrible a light as possible.
It is essential to remember that the Richard portrayed in this play is a fictional character, although one of the most compelling characters ever created. Shakespeare drew on the History of King Richard the Third by Thomas More as his primary source, but chose to heighten and embellish many details. More's version relied on that of Polydor Vergill for information, at the same time focusing on propagating the Tudor Myth. Thus the description of Richard as deformed, having been born with teeth, etc., is highly unlikely and is not born out in any analysis of existing portraits of Richard. Given the political environment, Shakespeare's dramatically enhanced account is actually quite partisan.
Richard III is the fourth part of a tetralogy which starts with Henry VI, Parts 1,2, and 3. The play derives much of its nature from the earlier Richard Duke of York in both the deformation of the Richard's body and the allusions to Machiavellian rule. Niccolo Machiavelli wrote The Prince in 1513 (printed in 1532) in which he explicitly supported the use of torture, lying, cheating, and hypocrisy by princes in order for them to achieve their goals. This appears in Richard III in several scenes, the most notable being when Richard appears with a prayer book in his hand while at the same time coordinating a popular call for his coronation.
The use of the machiavel in tragedy is similar to the role of Vice in a morality play. Indeed, Richard is actually a brilliant combination of these two roles, able to be both the machiavel and the humorous Vice. In an audience aside he comments, "Thus like the formal Vice, Iniquity,/ I moralize two meanings in one word" (3.1.82-83). Thus Richard is sometimes funny, othertimes erotic, charming, or terrifying. Shakespeare enforces this split by giving Richard two voices: that of Vice when he speaks in soliloque, and that of the machiavel when he interacts with the other characters. Later he is forced to merge these voices, particularly after assuming the throne.
There are three main explanations of Richard's behavior which are intensified in the play: political, psychological, and metaphysical. Politically Richard is a dictatorial schemer who sets out to destroy his rivals. Psychologically he mixes courage and genius with hate, while metaphysically he is seen to represent the devil. Shakespeare heightens each of these explanations by condensing years of action into simultaneous plots. For example, Richard's courtship of Lady Anne which really occurred in 1472 ends up happening at the same time that Richard plots against his brother Clarence (1478).
Richard III stands out as one of Shakespeare's most extreme plays in its use of theatricality. Each of the speeches indicates that the speakers are keenly self-aware of their roles. The audience quickly realizes that this is because the real play is staged and directed by Richard himself, who states as much in his opening lines: "To entertain these fair well-spoken days, / I am determined to prove a villain / And hate the idle pleasures of these days. / Plots have I laid, inductions dangerous" (1.1.29-32). Richard's plots do indeed prove dangerous, and Shakespeare's play within a play proves to be one of the most memorable ever made.