This volume, the third in a sequence that began with The Theory of Matroids and Combinatorial Geometries, concentrates on the applications of matroid theory to a variety of topics from geometry (rigidity and lattices), combinatorics (graphs, codes and designs) and operations research (the greedy algorithm). As with its predecessors, the contributors to this volume have written their articles to form a cohesive account so that the result is a volume which will be a valuable reference for research workers.