Translation generalized quadrangles play a key role in the theory of generalized quadrangles, comparable to the role of translation planes in the theory of projective and affine planes. The notion of translation generalized quadrangle is a local analogue of the more global “Moufang Condition”, a topic of great interest, also due to the classification of all Moufang polygons. Attention is thus paid to recent results in that direction, but also many of the most important results in the general theory of generalized quadrangles that appeared since 1984 are treated.Translation Generalized Quadrangles is essentially self-contained, as the reader is only expected to be familiar with some basic facts on finite generalized quadrangles. Proofs that are either too long or too technical are left out, or just sketched. The three standard works on generalized quadrangles are (co-)authored by the writers of this book: “Finite Generalized Quadrangles” (1984) by S E Payne and J A Thas, “Generalized Polygons” (1998) by H Van Maldeghem, and “Symmetry in Finite Generalized Quadrangles” (2004) by K Thas.Contents:Generalized QuadranglesRegularity, Antiregularity and 3-RegularityElation and Translation Generalized QuadranglesGeneralized Quadrangles and FlocksGood EggsGeneralized Quadrangles, Nets and the Axiom of VeblenOvoids and SubquadranglesTranslation Generalized OvalsMoufang Sets and Translation Moufang SetsConfigurations of Translation PointsMoufang Quadrangles with a Translation PointTranslation Ovoids in Translation QuadranglesTranslation Generalized Quadrangles in Projective SpaceOpen ProblemsReadership: Researchers in incidence geometry, combinatorics and finite geometries. Also suitable as a textbook for a graduate course.