How are Shakespeare's plays classified?
Shakespeare's plays are classified into three main groups: histories, comedies, and tragedies - though it's important to remember that these classifications are largely imposed by modern critics and weren't invented by Shakespeare.
For example, "Richard III" is usually considered a "history" by modern critics, where Shakespeare titles it "The Tragedy of Richard III". And, moreover, several of Shakespeare's comedies (including plays like, for example, the play which controversially deals with racism, "The Merchant of Venice") aren't particularly "comic". Classifying Shakespeare is very difficult: it's one of the reasons why he's so great.
The texts of the plays themselves fall into two categories. Most plays were published in 1623 (7 years after Shakespeare's death) in the First Folio - and are known as "Folio" versions of the plays. Quarto versions are often "illegal" copies - a bit like pirated DVDs or videos - perhaps scribbled down by actors, printed illegally by publishers - though sometimes were just a way of getting an edition of a single play to print fast. Folio and Quarto versions can differ substantially.