Analysis, Manifolds and Physics : Part I

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Summary: A treasure for physicists
Review: I use this book constantly. At first I thought it was good only as a reference, but now I know it is possible to actually LEARN any of its subjects from scratch. I particularly like its chapters on manifolds, Lie Groups and bundles. Connections on a principal bundle is extremely well done, with a translation to physics (gauge theories) performed in detail in an exercise (so to speak). Some time ago David Ruelle said that the physicists needed a presentation of recent mathematics in the form of Bourbaki's "Fascicule des resultats", a synthesis of the subject with complete definitions, examples and theorems clearly stated, but with the proofs ommited. This is it, except that in this book most demonstrations are not ommited, only those too complicated. The whole book is extremely readable, if you concentrate, turn out the TV, etc. A precious book.

Rating:
Summary: an inspiration
Review: This is the book that inspired me as an undergraduate to learn and appreciate, to a large extent, how physics and mathematics cohabit so beautifully. I continue to see, to this day, as a graduate student, how many of the recent developments in theoretical physics have been inspired by new mathematics and conversely. I still refer to this book on occasion, since it is laid out in a style that is amenable to mathematicians (such as myself!). It's an excellent read, and I highly recommend it (even as bed time reading!) Best regards, A.

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Summary: A must have desk reference and educational tool
Review: This was the most reliable (and compact) source of mathematical information that I could find. I used it (almost exclusively) to teach myself what I needed to know to do my PhD thesis in General Relativity with Torsion fields. It is very overwhelming to look at the book the first time. But give it time. It is well written and inviting. The only draw back for me was the very small print.