The Mathematical Olympiad books, covering the USA Mathematical Olympiad (USAMO) and the International Mathematical Olympiad (IMO), have been published annually by the MAA American Mathematics Competitions since 1976. This is the sixth volume in that series published by the MAA in its Problem Book series. Through the AMC contests and the IMO, young gifted mathematicians are identified and recognized while they are still in secondary school. Participation in these competitions provides them with the chance to measure themselves against other exceptional students from all over the world. This work was prepared by Zuming Feng, Melaine Wood, the Leader and Deputy Leader of the 2004 USA IMO team, and by Cecil Rousseau, the chair of the USAMO Committee. In addition to presenting their own carefully written solutions to the problems, Zuming and Po-Shen provide remarkable solutions developed by the examination committees, contestants, and experts, during or after the contests. They also provide a detailed report of the 2000-2004 USAMO/IMO results and a comprehensive guide to other materials that emphasize advanced problem-solving. This collection of excellent problems and beautiful solutions is a valuable companion for students who wish to develop their interest in mathematics outside the school curriculum and to deepen their knowledge of mathematics.