[.ca] Tensor Geometry: The Geometric Viewpoint and its Uses (ISBN 354052018X)

Serious math for mathematical readers, but excellent:
I found learning GR very frustrating, as I am a mathematician by training and found the woolly "picture the vector" approach of say Graviatation (Misner et al) very loose. it drove me crazy. When I found this I was pleased, and found thye rigourous footing I wanted for the subject. Bundles! After this I could read Gravitation with some comfort. NOT repeat NOT for anyone but mathematically trained readers.

Good introduction:
I agree with previous reviewers, and only wish to add a few comments: 1. This book assumes very little on the part of the reader, which makes it ideal for beginners, as long as they're mature readers. 2. Like many books out there, everything in this book is real and finite dimensional, which is a bit disappointing. 3. It's not as advanced as the writers or reviewers would like to think. For instance, no differential forms, no killing vectors, and although there's a chapter on lie groups it treats only their geometrical aspects and not the algebraic ones. 4. However, it contains two (extensive) chapters on SR and GR which are pure gold, I say! Everything is done from the geometrical point of view, and only AFTER all of the math has been introduced, so the discussion is mature and elegant. In short, this is a good book to read for the geometrical intuition but don't count on it to explain everything about differential geometry. Enjoy!

Excellent, But Has Flawed Editing:
I found this book much more comprehensible than the Bishop & Goldberg text (perhaps because the specifics of my particular graduate program made this approach more accessible). The only problem is that in some important areas of the text there are typographical errors; this text needs a new corrected edition--otherwise I have no complaints. The only recommendation I would make to a prospective reader is to obtain a copy of the excellent, old, out-of-print (but still readily avilable used, on the web) Vector and Tensor Analysis by Louis Brand and master the tensor chapter in it. This will prepare the reader to gain an idea of where the authors are heading with their modern, abstract functional analysis approach. The reader will be greatly assisted by a solid understanding of linear algebra and a preparatory course in functional analysis wouldn't hurt, either. This material is challenging even for a math graduate student; any high school student who could master this book would have to be gifted, indeed.

A must for mathematicians interested in cosmology:
Besides providing in clear-cut fashion the mathematics essential to research in cosmology, the authors simplify many concepts the physicists make opaque.

A great, usefull book that is easy to understand:
Considering the fact that I am a high school student and I had no problem understanding the majority of this text, I would call this book wonderful! It is a book that no student of general relativity or differential geometry can do without. It develops insightful geometric premises early on so that the whole picture of tensors can be absorbed, not just those "definitive" transformation equations. The book is not dry like most math books either. It contains almost witty sections as well as enlightening mathematical ideas. I would recommend this book to anyone studying tensors on their own, or as a supplementary text book for a class.