For advanced undergraduate or graduate level students with some elementary notions from graph theory, this text is intended as a rigorous, enticing introduction to be used in a one-semester course. Without attempting comprehensiveness and touching only lightly on applications, Lee (IBM T.J. Watson Research Center) discusses linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. He emphasizes the unifying roles of matroids, submodularity, and polyhedral combinatorics, and does not dwell on data structures and implementation details. Problems and exercises are included throughout.