Differential Geometry
A rigorous introduction to the geometry of curves and surfaces, built around the concept of curvature. Topics move from the classical theory of plane and space curves through the first and second fundamental forms of surfaces, Gaussian and mean curvature, geodesics, and the Gauss-Bonnet theorem connecting local curvature to global topology. The course keeps the treatment concrete, working through explicit examples and computations rather than staying purely abstract. Materials from MIT OpenCourseWare include lecture notes, problem sets, and exams covering the full term, letting students work through the derivations at their own pace. No enrollment or certificate is offered since this is a self-study OpenCourseWare release, but all course materials are free to use. Suited to students who have completed multivariable calculus and linear algebra and want a first serious encounter with differential geometry.