"A revised edition of the now classic text, Exact Solutions of Einstein's Field Equations gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It starts by introducing the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties." This edition has been expanded and updated to include the new developments in the field since the publication of the first edition. It contains five completely new chapters, covering topics such as generation methods and their application, colliding waves, classification of metrics by invariants and inhomogeneous cosmologies. It is an important source and guide for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. Parts of the book can also be used for preparing lectures and as an introductory text on some mathematical aspects of general relativity.