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The International Mathematical Olympiad competition is held every year with the final taking place in a different country. The final consists of a two day exam with the contestants being challenged to solve three difficult problems each day. This book contains the questions from the finals taking place between 1986 and 1999 inclusive. For each problem the author has included at least one solution and often remarks about alternative approaches and the significance of the problem. Many of the solutions are derived from answers given by contestants rather than the organisers as these were often the most elegant solutions. This collection will be of great value to students preparing for the IMO and to all others who are interested in problem solving in mathematics.