Here are some of the popular categories of books and stories in literature. An autobiography is the story of a person's life written or told by that person.

Bill Peet: An Autobiography
biography is the story of a person's life written or told by another person.
Eleanor, by Barbara Cooney
fable is a story that teaches a moral or a lesson. It often has animal characters.
The Tortoise and the Hare
Fantasy novels are often set in worlds much different from our own and usually include magic, sorcery and mythical creature.
The Harry Potter series by J. K. Rowling
folktale is a story that has been passed down, usually orally, within a culture. It may be based on superstition and feature supernatural characters. Folktales include fairy tales, tall tales, trickster tales and other stories passed down over generations.
Hansel and Gretel
legend is a story that has been handed down over generations and is believed to be based on history, though it typically mixes fact and fiction. The hero of a legend is usually a human.
King Arthur and the Roundtable
myth is a traditional story that a particular culture or group once accepted as sacred and true. It may center on a god or supernatural being and explain how something came to be, such as lightning or music or the world itself.
The Greek story of the Titan Prometheus bringing fire to humankind
Science fiction stories examine how science and technology affect the world. The books often involve fantasy inventions that may be reality in the future.
The Left Hand of Darkness, by Ursula Le Guin