I am very pleased with this book. The figures are black and white but extremely innovative. I think this masterpiece will become the modern MTW (Misner, Thorne, and Wheeler) of differential geometry. In other words: epic, legendary, enthusiastic without the MTW backdrop of taking the (presumably male) reader on any distasteful romantic conquests.<br><br>Back to the book at hand: very clever and insightful. I’ve looked at a few complex analysis and differential geometry books and have some familiarity with differential forms. I am definitely learning new things from this text.<br><br>The author’s genuine enthusiasm clearly shines through. Reading this book is unexpectedly delightful: like attending an impeccably planned opera while simultaneously listening to a professor spend an entire afternoon joyfully answering a question after a lecture.<br><br>Oh, and the index is very thorough! If what you are looking for is in the book, you will find a listing with every possible combination of ideas. I recommend reading the index to experience a thoughtful grouping of ideas in a new light. This is a 5-act book, but I’d call the index Act 6.<br><br>I have read the whole book at this point, and I will continue to browse for fun. I could also envision returning to pages with literal fruits and vegetables in figures: this book could serve as a kitchen laboratory manual for leisurely fruit peel curvature explorations. In addition, student-led math/science clubs could use the book as a starting point for developing public outreach demonstrations suitable for anyone old enough to chew fruit.