This book provides an upto date information on metric, connection and curva- ture symmetries used in geometry and physics. More specifically, we present the characterizations and classifications of Riemannian and Lorentzian manifolds (in particular, the spacetimes of general relativity) admitting metric (i.e., Killing, ho- mothetic and conformal), connection (i.e., affine conformal and projective) and curvature symmetries. Our approach, in this book,...