Robert Geroch's lecture notes on general relativity are unique in three main respects. First, the physics of general relativity and the mathematics, which describes it, are masterfully intertwined in such a way that both reinforce each other to facilitate the understanding of the most abstract and subtle issues. Second, the physical phenomena are first properly explained in terms of spacetime and then it is shown how they can be 'decomposed' into familiar quantities, expressed in terms of space and time, which are measured by an observer. Third, Geroch's successful pedagogical approach to teaching theoretical physics through visualization of even the most abstract concepts is fully applied in his lectures on general relativity by the use of around a hundred figures.
Although the book contains lecture notes written in 1972, it is (and will remain) an excellent introduction to general relativity, which covers its physical foundations, its mathematical formalism, the classical tests of its predictions, its application to cosmology, a number of specific and important issues (such as the initial value formulation of general relativity, signal propagation, time orientation, causality violation, singularity theorems, conformal transformations, and asymptotic structure of spacetime), and the early approaches to quantization of the gravitational field.
Geroch's Differential Geometry: 1972 Lecture Notes can serve as a very helpful companion to this book.
An Enduring Classic on General Relativity
By Robert J Kares on February 9, 2016
In the spring of 1972 when I was an undergraduate at the University of Chicago I had the great good fortune to attend a wonderful course of lectures on General Relativity given by professor Robert P. Geroch who was at that time newly arrived in Chicago from Princeton where he had been a PhD student of John Wheeler. The way in which that course was created remains an absolute amazement to me to this day. Professor Geroch would arrive at the lecture hall armed only with a single small white index card of notes, sometimes none at all, then pick up a piece of chalk and standing at the blackboard create a beautiful, clear explanation of some topic in General Relativity. When he was finished he would return to his office, roll carbon paper into his mechanical typewriter, and capture a prefect written version of the lecture which he had just given, then mimeograph it and hand it out at the next class meeting. As the class progressed through the spring quarter with lecture building upon lecture, a wonderful book on General Relativity took shape. I always expected that the University of Chicago Press would one day publish this book but for some reason it never did, and instead several generations of graduate students have had to content themselves with Xerox copies of these beautiful lecture notes instead. So you can imagine my surprise and delight when browsing Amazon one day to discover that the Minkowski Institute Press has published these notes as a book so that everyone can enjoy and learn from them.
This book is the clearest, most concise introduction to the General Theory of Relativity ever written. Here you will find General Relativity developed from first principles using Geroch's own unique and justly famous pedagogical approach to the subject. The geometrical spacetime reasoning is very intuitive and leads to a deeply satisfying understanding of the material. The coverage of topics is amazing for such a short volume. All the standard results including the Friedmann universes, the cosmological redshift, the Schwarzschild metric and the bending of light are derived in a compact, and elegant way. But the discussion also includes a large variety of advanced topics not usually found in a book at the introductory level. Chapter 34, for example, presents a simple proof of the singularity theorems that is really delightful.
Any serious student of General Relativity should own this book. And while the book may be read to great benefit on its own, I would suggest if you are a serious student, that you first buy and work through the companion volume, Geroch's 1972 Differential Geometry lecture notes which are also available in the same series from the Minkowski Institute Press. This is not required for reading the General Relativity lectures but it will certainly increase your understanding and enjoyment of them. And even if you are a mathematically sophisticated reader you should not neglect Geroch's delightful little non-mathematical book, General Relativity From A to B, University of Chicago Press, which really should be read as a companion to the General Relativity lecture notes.
If you want to learn General Relativity, then buy this book and work through it. You will be amazed at how much you learn in a short period of time, and the enduring value of the approach to the subject that it presents.
The physical (paper) book can be ordered from (for more options see):