Oriented matroids are a very natural mathematical concept which presents itself in many different guises, and which has connections and applications to many different areas. These include discrete and computational geometry, combinatorics, convexity, topology, algebraic geometry, operations research, computer science and theoretical chemistry. This is the first comprehensive and accessible account of the subject. This book is intended for a diverse audience: graduate students who wish to learn the subject from scratch, researchers in the various fields of application who want to concentrate on certain aspects of the theory, specialists who need a thorough reference work, and others at points in between. A list of exercises and open problems ends each chapter, and the work is rounded off by an up-to-date and exhaustive reference list.