With the advent of supercomputers, numerical relativity has become a prominent apparatus to investigate relativistic space-times. From cataclysmic processes that are experimentally inaccessible, such as gravitational collapses to black holes and neutron stars and the generation and propagation of gravitational waves, to the nonlinear growth of relativistic instabilities and beyond, numerical relativity addresses a wide range of multidimensional and nonlinear phenomena by providing algorithms to solve nontrivial systems of partial differential equations (PDEs) in space and time, especially Einstein’s equations.

This book provides a comprehensive reference on numerical relativity by familiarizing its readers with the fundamental concepts of general relativity and relevant numerical methods, with a view toward the most important applications.

The systematic development of the different subjects within the book is of great convenience. The first five chapters gradually introduce the two distinct types of gravitational field equations--the constraint and the evolution equations--and discuss different choices of coordinates, as well as the different relativistic stress-energy sources. After chapter 6’s brief but necessary review of the basic numerical methods for solving PDEs, the subsequent chapters thoroughly deal with black holes and gravitational waves in spherical and nonspherical space-times, followed by accurate discussions of the evolution of compact binaries (binary black holes, binary neutron stars, and binary black hole-neutron stars).

The authors recommend their book to students and researchers with a solid background in the basic theory of general relativity. However, based on the systematic organization of the book and its clear and adequate content, it could also be useful to those in other disciplines with related skills.