In 1935, Subrahmanyan Chandrasekhar challenged the prevailing theory of the day by suggesting that not all stars die the same death. He proposed that stars with more than 1.4 times the mass of the sun were compressed by their own gravitational forces into dense, dark objects. Winner of the 1983 Nobel Prize for Physics, Chandrasekhar here describes in exhaustive detail how a rotating black hole reacts to gravitational and electromagnetic waves--the forces associated with an infalling star. The author provides background material with a survey of the analytical methods necessary for the study of solutions that describe a rotating black hole, a derivation of the Schwartzschild metric of essential space-time features, and an account of how gravitational waves are scattered and absorbed. This is followed by a discussion of the Reisner-Nordstrom solution which predicts external and internal horizons and prepares the reader for the author's thorough treatment of the Kerr family of solutions. Beginning with the derivations of the Kerr metric, Chandrasekhar goes on to describe space-time in a Newman-Penrose formulation. He investigates such elements of the Kerr solution as geodesics and space-time--including the possibility of extracting energy from a rotating black hole, perturbations of the black hole with Maxwell's equations and the propagation of electromagnetic waves, gravitational perturbations, fields of spin-1/2 both massive and massless. His analysis shows that all relevant equations of mathematical physics allow explicit solutions in Kerr geometry. In the last chapter, Chandrasekhar deals with two other classes of solutions: axisymetric black hole solutions which are static but not asymptotically flat, and solutions which provide for an arbitrary number of isolated black holes, the relativistic analogue of the static equilibrium arrangement of Newtonian gravitational theory. This unique work encompasses not only the complete range of what is currently known about the properties of black holes, but the directions of future research.