Fundamentals of Differential Geometry (Graduate Texts in Mathematics, 191)

Rating:
Summary: Complete but lacking unity
Review: This book looks more like a big collection of essays than really a treatise on one subject. If you have read other books by Lang you will notice that some material included in previous works appears reproduced here word by word. Also, there are some inconsistencies in the notation of different sections, making it obvious that different parts of the book were written at different times, and perhaps by different persons.

All these shortcomings don't mean that the book is bad. Quite the opposite: It is a very complete survey on modern differential geometry, including from the fundamentals up to recent results. The graduate student and the working mathematician will find it very useful.