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.