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This book, the first volume in the DIMACS book series, contains the proceedings of the first DIMACS workshop. The workshop, which was held in June 1989 in Morristown, New Jersey, focused on polyhedral combinatorics. Two series of lectures were presented by L. Lovasz and A. Schrijver and there were a number of shorter lectures. The topics covered include multicommodity flows, graph matchings and colorings, the traveling salesman problem, integer programming, and complexity theory. Aimed at researchers in combinatorics and combinatorial optimization, this book will provide readers with an overview of recent advances in combinatorial optimization.