Let us know about books which should be added to this list.
- The USSR Olympiad Problem Book by N. Chentzov, et al - Excellent
practice for advanced competitions such as the USAMO and IMO. Problems
cover non-geometric topics such as number theory, inequalities, complex numbers, and more.
- USA and International Mathematical Olympiads by T. Andreescu & Z. Feng -
Problems and solutions from the USAMO & IMO. Written by two coaches
of the United States IMO team.
- The Mandelbrot Competition First Five Years by S. Vandervelde -
An excellent introduction to mathematical writing for beginning and
intermediate problem solvers; contains the Team Tests from the first
five years of the Mandelbrot Competition (go to Resources page at the
Mandelbrot site to learn how to purchase these past tests).
- Challenging Problems in Geometry by A. Posamentier, C. Salkind
- by T. Andreescu & Z. Feng. Problems (some with solutions, some without)
from 30 national and regional Olympiads from around the world.
- USA Mathematical Olympiads 1972-1986 Problems and Solutions by M. Klamkin
- The Canadian Mathematical Olympiad - Problems from the Canadian Olympiad from 1969-1993.
- Mathematical Olympiad Challenges by T. Andreescu, R. Gelca, M. Saul. Advanced
problems from the coach of the United States IMO team and a producer of ARML.
- The Mathematical Olympiad Handbook by A. Gardiner. Over 300 problems presented with
solutions from the British Mathematics Olympiad.
- More Mathematical Challenges: Problems for the UK Junior
Mathematical Olympiad by A. Gardiner, T. Gardiner.