This book had its beginnings over a decade ago, as a simple rewriting of Crapo and Rota's preliminary edition of Combinatorial Geometries, to be accomplished by Crapo, Rota, and White. We soon realized that the subject had grown enough, even then, that a more comprehensive compendium would be of greater benefit. This led, in turn, to the idea of soliciting contributions from many of the workers in matroid theory. Consequently, this work has grown too lengthy to be contained in a single volume. This is but the first of a projected three-volume series, although we are giving separate titles to each of the volumes. We are planning to call the remaining volumes Combinatorial Geometries, and Advances in Matroid Theory.

This first volume is a primer in the basic axioms and constructions of matroids. It will prove useful as a text because exposition has been kept a prime consideration throughout. Proofs of theorems are often omitted, with references given to the original works, and exercises are included. This volume will also be useful as a reference work for matroid theorists, especially Brylawski's encyclopedic chapter “Constructions” and his cryptomorphism appendix.

The volume starts with Crapo's chapter “Examples and Basic Concepts.” This chapter is a very informal introduction to matroids, with lots of examples, that provides an overview of the subject. The next chapter is “Axiom Systems,” by Nicoletti and White. This gets into the necessary work of proving the equivalence of some of the major axiom systems, a chore made easier by keeping in mind the familiar analogous concepts from linear algebra.