The course gives an introduction to differential geometry with a focus on Riemannian geometry. Starting with the geometry of curves and surfaces in the three-dimensional Euclidean space and Riemannian metrics in 2 and higher dimensions, the course introduces the first fundamental form, tangent bundles, vector fields, distance functions and geodesics, followed by covariant derivatives and second fundamental form. The proof of Gauss’s Theorema Egregium is highlighted. Additional topics are by instructor’s discretion. Students may not receive credit for both MA 489X and MA 4895.