This is the third volume of problems that cover the USA Mathematical Olympiad (USAMO) and the International Mathematical Olympiad (IMO) to be published by the MAA in its Problem Book series. The aims of the IMO are: to discover, encourage and challenge mathematically gifted young people in all countries; to foster friendships between mathematicians around the world; and to create an opportunity for the exchange of information on school syllabi and practice throughout the world. The USAMO and the Team Selection Test (TST) are the last two stages of the selection process leading to representing the USA in the IMO. The preceding examinations are the AMC 10 or AMC 12 and the American Invitational Mathematics Examination (AIME). Participation in the AIME, USAMO, and the TST is by invitation only, based on performance in the preceding exams of the sequence. All of these contests identify and recognize young gifted mathematicians 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.