This textbook set offers both an introduction to differential geometry designed for readers interested in modern geometry processing, as well as an exploration of more advanced topics. In the first volume, the authors work from basic undergraduate prerequisites to develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind...