* Book 1: Water
* Book 2: Earth
* Book 3: Fire
The story concluded with the defeat of the Fire Lord and the restoration of balance to the world. There was no need for a fourth book to further the story, as the main narrative was complete.
However, the Avatar universe has continued with:
* The Legend of Korra, a sequel series that follows the adventures of a new Avatar, Korra, who is from the Southern Water Tribe.
* Various comics, graphic novels, and other media that expand on the lore and characters of the Avatar world.
So, while there was no cancelled book 4, the Avatar universe continues to grow and evolve with new stories and characters.