Einstein's general theory of relativity requires a curved space for the description of the physical world. If one wishes to go beyond superficial discussions of the physical relations involved, one needs to set up precise equations for handling curved space. The well-established mathematical technique that accomplishes this is clearly described in this classic book by Nobel Laureate P.A.M. Dirac. Based on a series of lectures given by Dirac at Florida State University, and intended for the advanced undergraduate, General Theory of Relativity comprises thirty-five compact chapters that take the reader point-by- point through the necessary steps for understanding general relativity.
When I was first studying General Relativity, a graduate student friend of mine remarked that this little book has about all the information that "Gravitation" (http://www.amazon.com/Gravitation-Phy... - THE textbook on General relativity) has in just a fraction of the pages. He was only partly wrong, and this slim volume continues to be the best summary of this mathematically challenging field. Whenever I need a quick (and not so quick) reference for one of the basic results in General Relativity, this is the first place where I look. Either as a secondary reference or the first textbook on the field, this book continues to be a valuable resource.
Possibly useful as a reference, but the simplifications used to render the presentation compact obscure distinctions that make the book largely worthless to anyone who has not already seen the details before.
I should note that the book may be of more use to Physicists learning general relativity as opposed to Mathematicians learning the subject. I am, sadly, in the latter category.
Wonderful introduction to the Math needed for understanding General Relativity. I am a grad student pursuing my PhD in Math and I have seen quite a bit of Differential Geometry earlier, too. Yet, I think this book can be followed quite easily by mathematicians and non-mathematicians alike. It's power packed with all the essential elementary results needed for a proper study of GR.
This is a masterpiece of terseness. There is not a single diagram in the entire book which is serious defect. Not useful as an introduction, but possibly useful as a reference if you need to look up definitions, formulas, and calculaltions. On the plus side, I did learn a new way to think about parallel transport for submanifolds of Euclidean spaces.