This book is definitely a must for the mathematically minded physicist. Self-contained, logically structured throughout, absolutely consistent mathematical notation (which nevertheless does not slide into over-sophistication). It is as if Frankel somehow knew about the anger of readers who are never satisfied with the mathematical presentation within similar textbooks. The covered material is the right collection of things that are 'needed' nowadays and missing topics can easily be added by reading sections in Nakahara (which is the best supplementary text). In comparison to Nakahara, Frankel is much more rigorous and precise. For instance the notion of 'tensor product' and its relation to the wedge-product of p-forms is not properly handled in Nakahara, also, Nakahara usually does not motivate the mathematical need of a new construction. Probably only a pure mathematician may find inconsitencies or unsatisfactory conclusions in Frankel's book.
I do not agree to the previous review that Frankel is not suited for self study. On the contrary, Frankel is THE book for self study, it's a pleasure to go through it page by page. Only real requirement: you must like the field. So if you have a sort of a 'feeling' for the strange beauty of topology and manifolds, then this is the book for you. The nice thing about it is that it nevertheless provides 'practical' knowledge, ie. the reader really learns how to use the mathematical concepts 'practically' with paper and pencil. Frankel is right when he claims in his preface that this volume provides a 'working knowledge' of the mathematical tools. Proofs are given almost throughout and only in cases where they encourage mathematical thinking, otherwise the reader is referred to the original literature. Frankel clearly explains why and when 'classical' theoretical physics notation may lead to errors and misinterpretations in comparison to the modern language of geometry where these problems cannot occur.
You will see that Frankel liked writing this book and teaching you, the reader --quite a seldom luxury I would say.
Congratulations to Frankel for this excellent textbook of mathematical physics, I can only hope that it will set a standard worldwide. I definitely recommend it without restriction to readers and librarians.