This book serves two purposes. The authors present important aspects of modern research on the mathematical structure of Einstein's field equations and they show how to extract their physical content from them by mathematically exact methods. The essays are devoted to exact solutions and to the Cauchy problem of the field equations as well as to post-Newtonian approximations that have direct physical implications. Further topics concern quantum gravity and optics in gravitational fields.The book addresses researchers in relativity and differential geometry but can also be used as additional reading material for graduate students. TOC:From the contents: The Role of Exact Solutions of Einstein's Equations in the Developments of General Relativity and Astrophysics Selected Themes.- The Cauchy Problem of the Einstein Equations.- Gravitational Radiation in the Post-Newtonian Approximation.- Duality and Hidden Symmetries in Gravitational Theories.- Time-Independent Gravitational Fields.- Gravitational Lensing from a Geometric Viewpoint.
Selected Solutions of Einstein's Field Equations: Their Role in General Relativity and Astrophysics.- The Cauchy Problem for the Einstein Equations.- Post-Newtonian Gravitational Radiation.- Duality and Hidden Symmetries in Gravitational Theories.- Time-Independent Gravitational Fields.- Gravitational Lensing from a Geometric Viewpoint.