There are many different types of literary genres. The most common are listed below.
- Fairy Tale
- Historical Fiction
- Myths & Legends
- Science Fiction
- Short Stories
We can also include other genres that are perhaps not so common or widely known, such as the Bildungsroman. It's very difficult to make a list of genres because "genre" is a far-reaching term. If I were to make a list of categories for students, there are lots of different categories I could apply, and all of them would be correct.
So--when your teacher asks you to classify a work, take it slow. Begin with the three main genres. Is the work poetry, prose, or nonfiction?
Next, begin trying to break the work down into other categories. Is the work set in a certain time period? Perhaps it's historical fiction. Does it center around a specific type of character, like a slave narrative?
Generally, if the novel has a very specific genre (Bildungsroman, satire, etc.), your teacher will let you know (or guide you to that conclusion). However, you should be able to identify basic genres like those in the list above on your own.