A Short Course in General Relativity

Rating:
Summary: Choice Book to Start Off In
Review: A truly great introduction to GR. If anything, it quickly puts you into the fold of doing the mathematics (and physics ) of GR. Not too many applications are discussed, which is a PLUS in this case. Many times, the mathematics and the physics can be overwhelming. This books helps lessen this considerably.

It's also a good pre-study to Schultz. Schultz is also an excellent book, but Foster's focuses on the immediate 'necessities'. Great for a first course in general relativity, or for the self learner who wants to see what's up with GR (of course vector calculus is assumed, but not too much more).

Rating:
Summary: Great for independant study
Review: As a person who did postgrad physics and maths over 5 years ago and has been out of the field for way too long, I found that this was a great introduction to GR, a subject I never got to do at university. It introduces the maths (tensors, manifolds and geodesics) in the earlier chapters and relies heavily on them in the introduction to GR.

The book has great solutions, or at least very helpful hints, to the problems that are given throughout the book. Though at times I was stuck with some, it generally it required me to only look at the first step of the solution to be able to solve the problem.

This book is a quantitative approach, while "A First Course in General Relativity" (Schutz) is a more qualitative approach. I personally perfer the quantitative approach, and found this book better than Schutz. If you're looking for a more verbose and wordy book, go for Schutz, while if you're going for a mathematical approach (includes the derivation of the Schwarzchild's solution and the rise of black holes coming from Schwarzchild's solution) then this book is more for you.

Rating:
Summary: A great first book on general relativity
Review: I like this book because it has the best elementary introduction to the mathematics of general relativity. It starts out with simple multivariable calculus and geometric notions about vectors. It then explains the ideas of the natural basis and the dual basis, first in a plane and then on a manifold, with very helpful figures. With too many other books it is possible in a first exposure to completely miss the point of these ideas, which really are pretty simple when you come right down to it. It is true that the physical motivation and meaning of general relativity are not treated in that much depth, but these can be picked up from other sources. In my view it is the mathematics that is the most intimidating thing about general relativity -- the physical ideas are exhilirating and natural by comparison!

Rating:
Summary: I couldn't use it.
Review: This book has everything I found to be correct in a text book but when I tried to teach with it I found it to have a lot of mathematics and not much of physical ideas.
Landau's Classical Field Theory book is much better but it is for advanced level, so I still didn't find a proper book.
Now I will try Schutz one.

Rating:
Summary: A well-balanced, readable introduction to GR.
Review: This book picks up with a brief refresher invector calculus and then proceeds to developthe differential geometry needed to treat the subject with fidelity. Interesting topics are supplemented with useful excercises, all with a minimum of wandering by the authors. This book is probably appropriate for a 4th year undergraduate or a 1st year graduate student in mathematics or physics -- excellent text for individual study.

Rating:
Summary: Useless
Review: This is a real gem. I have copies of both the first and second editions. The style is clear and concise with lots of 'do-able' exercises and problems. The mathematics required for understanding curvature is well explained in both editions, although the authors seemed to think that the first edition placed too many demands on the reader for a first course in GR.There is a nice balance between explaining the mathematics fully (without getting bogged down with inappropriate rigour) and the usual physical applications. The second edition that I have does not include solutions/hints for the exercises but one of the authors (J.Foster) kindly provided a little booklet upon request. This book is very accessible for independent study.

Rating:
Summary: An Excellent Book
Review: This is one gem of a book! It's paced extremely well--the authors managed to write a book which is neither cryptic from lack of detail nor cumbersome with too much detail. It strikes me as the perfect self study book for a physics or mathematics student.

You won't find the ramblings of 'The Phone Book', nor will you find the obfuscated discussions in Wald. If you like David Griffiths' friendly and breezy writing style, you'll love this book.

Don't let its size fool you. While the book is short in pages, it manages to cover most of what Schutz's book covers (another great book) and in many cases, does it better.

I'd say it's suitable for a motivated junior undergraduate and is certainly suitable for a graduate student at any level.

It has my full recommendation.