The International Mathematical Olympiad (IMO) is the World Championship Competition for High School students, and is held annually in a different country. More than eighty countries are involved. Containing numerous exercises, illustrations, hints and solutions, presented in a lucid and thought- provoking style, this text provides a wide range of skills required in competitions such as the Mathematical Olympiad. More than fifty problems in Euclidean geometry invo9lving integers and rational numbers are presented. Early chapters cover elementary problems while later sections break new ground in certain areas and area greater challenge for the more adventurous reader. The text is ideal for Mathematical Olympiad training and also serves as a supplementary text for student in pure mathematics, particularly number theory and geometry. Dr. Christopher Bradley was formerly a Fellow and Tutor in Mathematics at Jesus College, Oxford, Deputy Leader of the British Mathematical Olympiad Team and for several years Secretary of the British Mathematical Olympiad Committee.