This volume first appeared in the English and Russian editions in 1974 as an introduction for new graduate students, to the rapidly developing field of relativistic astrophysics and cosmology. Some of the classic concepts introduced in the first edition included: * the lines of force of electric and magnetic fields near a black hole * the ergosphere and effective potential techniques for a rotating black hole * the details of rotational energy extraction from a black hole * the basic estimates for the cross-sections of gravitational wave detectors * and for the energy sources of gravitational waves * the scenario for gravitational collapse In cosmology, the foundations of the hot big bang model, the cosmic background radiation and cosmological nucleosynthesis were reviewed and the volume concluded with a lecture entitled Beyond the End of Time by J.A. Wheeler. Since 1974, enormous progress has occurred in some of these areas and the corresponding treatments are complex. This new edition provides a useful source of reference and presents the initial treatments of these topics and the ideas that motivated them thus providing a more complete picture of the development of this field for the reader. In order to mark the progress made in the intervening years, the authors have compiled a introduction to the new edition and an Appendix which comprises classic reprints which are related to the problems discussed in the original edition.