The International Mathematical Olympiad (IMO) is the most prestigious competition for high-school students interested in mathematics. It offers high school students a chance to measure up with students from the rest of the world. This book attempts to gather all the problems and solutions appearing on the IMO over the past fifty years and to present them in one volume for the first time. It is the result of a two year long collaboration between former IMO participants to rescue these problems from old and scattered manuscripts, and produce the definitive source of IMO practice problems. In short, "The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems. With a grand total of 1900 problems this book is an invaluable resource for high-school students preparing for mathematics competitions, and for anyone who appreciates and loves math.