This book is an introduction to differential geometry and a suitable companion to the differential geometry module (one or two semesters). It begins with classical aspects such as the geometry of curves and surfaces, before moving on to higher-dimensional surfaces and abstract manifolds. The connecting point is the central chapter "The Inner Geometry of Surfaces," which leads the reader to the famous Gauss-Bonnet theorem, a crucial link between local and global geometry. The second half of the book is dedicated to Riemannian geometry. It concludes with a chapter on "Einstein Spaces," which hold significant importance in both pure mathematics and A. Einstein's general relativity. Emphasis is placed on clarity, supported by numerous illustrations.