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This book is a collection of six articles arising from the meeting of the NATO Advanced Study Institute (ASI) ''Combinatorial Optimization: Methods and Applications,'' which was held at the University of Montreal in June 2006. This ASI consisted of seven series of five one-hour lectures and one series of four one-hour lectures. It was attended by some sixty students of graduate or postdoctoral level from fifteen countries worldwide. Topics include: integer and mixed integer programming, facility location, branching on split disjunctions, convexity in combinatorial optimization, and VLSI design. Although drawn from the 2006 lecture series, the articles included in this volume were all either written or updated by the authors in 2010, so that this collection of papers reflects a state-of-the-art overview of combinatorial optimization methods and their applications