During 199697 MSRI held a full academic year program on Combinatorics, with special emphasis on the connections with other branches of mathematics, such as algebraic geometry, topology, commutative algebra, representation theory, and convex geometry. The rich combinatorial problems arising from the study of various algebraic structures are the subject of this book, which represents work done or presented at seminars during the program. It contains contributions on matroid bundles, combinatorial representation theory, lattice points in polyhedra, bilinear forms, combinatorial differential topology and geometry, Macdonald polynomials and geometry, enumeration of matchings, the generalized Baues problem, and LittlewoodRichardson semigroups. These expository articles, written by some of the most respected researchers in the field, will present the state of the art to graduate students and researchers in combinatorics as well as algebra, geometry, and topology.