A paperback edition of a classic text, 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 introduces 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. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity.

‘… not only is the book an unrivalled source of knowledge on what has been charted of the rugged landscape of curved space-times, but, additionally, it is a well-organized and concise reference in matters of differential geometry.’

Source: General Relativity and Gravitation

‘… a remarkable work, and indispensable to any serious practitioner of classical general relativity.’

Source: Mathematics Today

‘… will be a lighthouse for those navigating in the ever expanding ocean of exact solutions to Einstein's equations.’

Source: Zentralblatt MATH

‘This is clearly a most valuable reference book. It comprehensively reviews known local solutions of Einstein's equation and provides a secure base for future research.’

Source: Mathematical Reviews

'We should be thankful to the authors for having undertaken this project. The second edition, like the first one, is a real masterpiece.'

Source: CERN Courier