The author's name is well known to theoretical physicists and cosmologists. Penrose is the author of the proof of an important theorem about the inevitability of the physical singularity of space-time during the relativistic collapse of bodies. This small book outlines the problems of general relativity, including the nature of general relativity, Conformal Infinity , Particle and Event Horizons , Relativistic Gravitational Collapse and the Role of Singularities in Cosmology , and the methods developed by the author to analyze the structure of space-time. The book is of great interest to theoretical physicists, astrophysicists, cosmologists - both specialists and senior students of higher educational institutions and graduate students ..