This textbook provides a modern introduction to differential geometry, roughly equivalent to a one-semester course. It initially addresses the geometry of surfaces in space. Numerous examples train readers in geometric intuition, with minimal surfaces being the most important class. To study these, the authors develop analytical methods and solve the Plateau problem in this context, which involves finding a minimal surface with a given boundary. As an example of a global statement in differential geometry, they prove Bernstein's theorem. Further chapters cover the intrinsic geometry of surfaces, including the Gauss-Bonnet theorem, and present hyperbolic geometry in detail. The authors connect geometric constructions with analytical methods, following a central trend in modern mathematical research.