There are many literary genres. In light of this, let me name a few of them.
First, perhaps the biggest division in literature is the division between prose and poetry. What make something poetry is usually the meter. Prose, on the other hand, is not written in any formal pattern.
Second, within poetry, there are many genres, and tragedies and comedies are two of them. As an example, Sophocles' Oedipus Rex would be one of the most famous tragedies, and Aristophanes', Frogs would be an example of a comedy.
Third, with history, there are biography, autobiographies, ethnographies, and commentaries, to name a few historical genres.
As you can see, there are many genres.
poetry, fiction, essay and drama