Disclaimer: This review is provided by someone who already has a working knowledge of differential geometry.The book introduces the reader to several abstract constructions on a general smooth manifold firstly on affine spaces. This is the viewpoint the book sticks to for the first 9 chapters. Starting in Chapter 10, these ideas are generalized to arbitrary smooth manifolds. I think this approach facilitates internalizing and learning the material immensely. I believe I would have had a much smoother and easier time understanding the core concepts in differential geometry if I had come across this book early in my graduate school days.The book has a good deal of exercises spread around in each chapter. Some of these exercises bolster the understanding of the material, while some of them are designed to get the readers to add some material which are alluded to or used later in the book. The exercises are usually not difficult and are concise -- they should be considered as part of the textbook and tackled as soon as possible.The final few chapters of the book delve more into the theory of classical mechanics formulated in a coordinate-independent manner and finish with principal bundle structures. The exposition is again quite succinct and is at least as entertaining to read and study as the classic books of Kobayashi and Nomizu.