Symmetry in finite generalized quadrangles In this monograph finite generalized quadrangles are classified by symmetry generalizing the celebrated Lenz Barlotti classification for projective planes. The book is self contained and serves as introduction to the combinatorial geometrical and group theoretical concepts that arise in the classification and in the general theory of finite generalized quadrangles including automorphism groups elation and translation generalized quadrangles generalized ovals and generalized ovoids span symmetric generalized quadrangles flock geometry and property (G) regularity and nets split BN pairs of rank 1 and the Moufang property. Introduction: History Motivation 1. Finite Generalized Quadrangles 2. Elation Generalized Quadrangles Translation Generalized Quadrangles and Flocks 3. The Known Generalized Quadrangles 4. Substructures of Finite Nets 5. Symmetry Class I: Generalized Quadrangles with Axes of Symmetry 6. Symmetry Class II: Concurrent Axes of Symmetry in Generalized Quadrangles 7. Symmetry Class II: Span Symmetric Generalized Quadrangles 8. Generalized Quadrangles with Distinct Translation Points 9. The Classification Theorem 10. Symmetry Class IV.3: TGQs which Arise from Flocks 11. A Characterization Theorem and a Classification Theorem 12. Symmetry Class V 13. Recapitulation of the Classification Theorem 14. Semi Quadrangles Appendices References.