Generalized quadrangles (GQ) were formally introduced by J. Tits in 1959 to describe geometric properties of simple groups of Lie type of rank 2. The first edition of Finite Generalized Quadrangles (FGQ) quickly became the standard reference for finite GQ. The second edition is essentially a reprint of the first edition. It is a careful rendering into LaTeX of the original, along with an appendix that brings to the attention of the reader those major new results pertaining to GQ, especially in those areas where the authors of this work have made a contribution. The first edition has been out of print for many years. The new edition makes available again this classical reference in the rapidly increasing field of finite geometries. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in generalized quadrangles. Table of Contents  Combinatorics of finite generalized quadrangles
 Subquadrangles
 The known generalized quadrangles and their properties
 Generalized quadrangles in finite projective spaces
 Combinatorial characterizations of the known generalized quadrangles
 Generalized quadrangles with small parameters
 Generalized quadrangles in finite affine spaces
 Elation generalized quadrangles and translation generalized quadrangles
 Moufang conditions
 Generalized quadrangles as group coset geometries
 Coordinatization of generalized quadrangles with \(s=t\)
 Generalized quadrangles as amalgamations of desarguesian planes
 Generalizations and related topics
 Appendix. Development of the theory of GQ since 1983
 Bibliography
 Index
