A Course in Differential Geometry

A Course in Differential Geometry studies the shapes, curves, and surfaces that exist in space using mathematical techniques. It explores how these objects bend, twist, and relate to each other, providing tools to analyze their properties beyond simple measurements. By applying calculus and algebra, it helps us understand complex forms like curves in three dimensions, surfaces like spheres or tori, and more abstract spaces. This field underpins many scientific and engineering applications, including computer graphics, physics (like general relativity), and robotics, offering a precise way to describe and analyze the geometry of the world around us.