102 carefully selected problems (with solutions) used to train and test the USA International Mathematical Olympiad (IMO) team are presented here. Undergraduates in combinatorics and tangential areas and advanced high school students will find a stimulating, practical choice of topics, including combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities.