This text provides information on metric (i.e. Killing, homothetic and conformal), connection (i.e. affine, conformal and projective), curvature collineations and curvature inheritance symmetries. It attempts to present not only a comprehensive account of a very large number of papers on symmetries of spacetimes and Riemannian manifolds, but also the Lie group/algebra structures of symmetry vectors, their kinematics/dynamics, compact hypersurfaces (dealing with the initial value problem in general relativity) and lightlike hypersurfaces. This book also contains information on symmetries of Kaehler, contact and globally framed manifolds.