Discuss the use of humour in Richard III.
You are right in identifying that this play, in spite of its status as a historical tragedy with a focus on evil in the person of its title character, is actually full of plenty of examples of humour. However, it is appropriate that this humour, as befitting the overall tone and mood of the play, is darkly funny and consists mainly of black humour. Most of the humour is based around Richard's ability to laugh and make fun of himself, but also there are various examples of how he ridicules those who foolishly place confidence in him.
For example, you might like to consider the way in which dramatic irony adds to the humour of the play. For example, in Act I scene 1, Richard makes many kind and caring comments to his brother Clarence as he is being taken to prison, even though we know that Richard is actually the one responsible for Clarence being locked up in the first place.
Secondly, parody is used by Richard at various stages to poke fun at someone or something that is meant to be treated with a serious attitude. This is perhaps most clearly seen when Richard parodies both himself and Anne following the success of his romantic overtures. Note how he makes fun of himself in the following lines from Act I scene 2:
I'll be at charges for a looking-glass,
And entertain a score or two of tailors
To study fashions to adorn my body.
Richard, therefore, although he is a figure of evil, is nonetheless somebody who manages to present an often grimly humorous take on what happens in the play and his own conduct, even being willing to make fun of himself to add to the comedy.