Brisingr is the third book in Paolini's Inheritance series. The first two are Eragon and Eldest. This is an excellent series for children old enough for the books. I've already purchased the first two books in paperback for some of my grandchildren to read. I'll add Brisingr to that list when it comes out in paperback.
The Inheritance series follows a young boy, Eragon, as he discovers a dragon egg and grows to become the first free dragon rider of his generation. Eragon is human, but in the world of these books there are elves, dwarves, urgals, and more. In Brisingr, Eragon and his dragon Saphira rescue a maiden, defeat a corrupt dragon and rider, help pick a dwarf king, forge a new sword, and discover what might be the key to defeating the evil Galbatorix. Please read these wonderful books in the right order. Highly recommended.