Memoirs of the American Mathematical Society 2005; 99 pp; softcover Volume: 173 ISBN10: 0821836080 ISBN13: 9780821836088 List Price: US$66 Individual Members: US$39.60 Institutional Members: US$52.80 Order Code: MEMO/173/818
 Very recently, the classification of Moufang polygons has been completed by Tits and Weiss. Moufang \(n\)gons exist for \(n \in \{ 3, 4, 6, 8 \}\) only. For \(n \in \{ 3, 6, 8 \}\), the proof is nicely divided into two parts: first, it is shown that a Moufang \(n\)gon can be parametrized by a certain interesting algebraic structure, and secondly, these algebraic structures are classified. The classification of Moufang quadrangles \((n=4)\) is not organized in this way due to the absence of a suitable algebraic structure. The goal of this article is to present such a uniform algebraic structure for Moufang quadrangles, and to classify these structures without referring back to the original Moufang quadrangles from which they arise, thereby also providing a new proof for the classification of Moufang quadrangles, which does consist of the division into these two parts. We hope that these algebraic structures will prove to be interesting in their own right. Readership Graduate students and research mathematicians interested in algebra and algebraic geometry. Table of Contents  Introduction
 Definition
 Some identities
 From quadrangular systems to Moufang quadrangles
 From Moufang quadrangles to quadrangular systems
 Some remarks
 Examples
 The classification
 Appendix A. Abelian quadrangular systems
 Bibliography
