Relativistic cosmology has in recent years become one of the most active and exciting branches of research, often considered to be today where particle physics was forty years ago, with major discoveries just waiting to happen. Consequently the part most affected by this second edition is the last part on cosmology. But there are additions, improvements, and new exercises throughout. The book's basic purpose is unchanged. It is to make relativity come alive conceptually, and to display the grand theoretical edifice that it is, with consequences in many branches of physics. The emphasis is on the foundations, on the logical subtleties, and on presenting the necessary mathematics - including differential geometry and tensors - but always as late and in as palatable a form as possible. Aided by over 300 exercises, the book seeks to promote an in-depth understanding, and the confidence to tackle any basic problem in relativity.