This book is a text on classical general relativity from a geometrical viewpoint. Introductory chapters are provided on algebra, topology and manifold theory together with a chapter on the basic ideas of space-time manifolds and Einstein's theory. There is a detailed account of algebraic structures and tensor classification in general relativity and also of the relationships between the metric, connection and curvature structures on space-times, the latter includes chapters on holonomy and sectional curvature. An extensive study is provided of symmetries in general relativity including isometries, homothetoes, conformal symmetries and affine and curvature collineations. Several general properties of such symmetries are studied and an introductory chapter on transformation groups on manifolds is provided.