This book presents an elementary introduction to the theory of oriented matroids. The way
oriented matroids are introduced emphasizes that they are the most general - and hence simplest
- structures for which Linear Programming Duality results can be stated and proved. The main
theme of the book is duality. Using Farkas' Lemma as the basis the authors start with results
on polyhedra in Rn and show how to restate the essence of the proofs in terms of sign patterns
of oriented matroids. Most of the standard material in Linear Programming is presented in the
setting of real space as well as in the more abstract theory of oriented matroids. This
approach clarifies the theory behind Linear Programming and proofs become simpler. The last
part of the book deals with the facial structure of polytopes respectively their oriented
matroid counterparts. It is an introduction to more advanced topics in oriented matroid theory.
Each chapter contains suggestions for further reading and the references provide an overview of
the research in this field.
