Students just getting started with Olympiad-level problem solving should begin with Volume 2 of our Art of Problem Solving.

When you have command of the fundamentals and are ready to move on to more challenging Olympiad problems, we recommend The Art and Craft of Problem Solving by Paul Zeitz followed by Problem-Solving Strategies by Engel.

Other books of interest for Olympiad problem solvers can be found in the For the Pros section here.