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Now expanded and updated, this book 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 with an introductory part on the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions (Petrov classification, Newman-Penrose formalism, groups of motions or homotheties, prolongations and generation techniques). 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. A chapter is devoted to the application of generation methods. Following the success of the first edition, this book will be an important source and guide for researchers working in Relativity and in Mathematical and Theoretical Physics and Astrophysics.

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