"Oh my God! I wish I had this book when I was in college. Not only does it explain important mathematical principles better, but it explains principles I didn't even know were principles." --Ed Catmull, former president of Pixar and Disney Animation Studios "I love this book: profound mathematics, accessibly presented in plain relaxed English, caring in equal measure for both rigor and intuition. Visual Differential Geometry and Forms is elegant, beautifully typeset, deftly illustrated, and lovingly crafted. Needham masterfully puts geometry back in charge of mathematics, and he shows us that geometry still has some new things to tell us." --Bernard Schutz, Cardiff University "Here are five hundred eloquent pages packed with mathematical wisdom and deeply rooted in history. Visual Differential Geometry and Forms is visual indeed, with parallel transport, curvature, and geodesics depicted through pomelos, durians, squashes, pumpkins, potatoes, and toothpicks. I wish I'd had Needham's book when I was a student.

" --Michael Berry, University of Bristol, Europe "The tale of geometry--from ancient Greek struggles with the parallel postulate to Einstein's amazing discovery that space and time are curved--is rich, fascinating, and very much still in progress. Textbooks on geometry often present a dry, abbreviated version of this wonderful story. Not so with Needham's book: here, he narrates everything in detail while explaining the math with hundreds of pictures." --John Baez, University of California, Riverside "With many explanations that were wonderfully new for me, this book brilliantly succeeds in providing a truly geometric visual explication of differential geometry. Needham's writing style is magnificent, and the scholarship is impeccable. The treatment of general relativity, perhaps the most striking application of differential geometry, is splendid. I know of nothing like this work in the literature." --Frank Morgan, Williams College "A tour de force! This comprehensive treatment of introductory differential geometry actually emphasizes geometry , while providing clear explanations of the underlying concepts.

Best of all are the many original figures. Recommended for motivated novices and experts alike as a guide to what differential geometry is really about." -- Tevian Dray, Oregon State University "This unorthodox and highly original treatise on differential geometry eschews 'rigor' in the pedantic sense of the word--instead, it presents geometric proofs that are illuminating and instructive. Needham's book makes a great supplement to a standard textbook on differential geometry." --Loring Tu, author of Introductory Lectures on Equivariant Cohomology "Presenting a geometric exposition of differential geometry, this eloquently written book has a very clear and logical organization. The figures are nothing short of magnificent." --David A. Singer, Case Western Reserve University.