Robert Geroch's lecture notes on differential geometry reflect his original and successful style of teaching - explaining abstract concepts with the help of intuitive examples and many figures. The book introduces the most important concepts of differential geometry and can be used for self-study since each chapter contains examples and exercises, plus test and examination problems which are given in the Appendix. As these lecture notes are written by a theoretical physicist, who is an expert in general relativity, they can serve as a very helpful companion to Geroch's excellent "General 1972 Lecture Notes."
A really unique, engaging, and clear approach to the subject. While it was not exhaustive - focusing on topics which are used directly (or tangentially) in general relativity - there is certainly enough material here to constitute a full overview of the essentials of the topic. The examples were great, always clarifying. There were a few frustrating typos here and there, but given the quality of the content and the extremely reasonable price, I would certainly recommend this to both mathematicians and physicists interested in the topic.