Provides an extensive exploration of both classical and discrete differential geometry, focusing on their fundamental principles and practical applications. The book offers a clear framework for understanding the geometry of smooth curves, surfaces, and higher-dimensional objects, combining both traditional and modern approaches. It begins with an introduction to classical differential geometry, including key concepts such as curvature, torsion, geodesics, and the Gauss-Bonnet theorem. These classical methods are essential for studying the properties of smooth manifolds and the behavior of surfaces in higher-dimensional spaces.