The book outlines the differential geometry of curves and surfaces from basic concepts to subtle theorems about global structure. A feature of the book is the reader's familiarization with the basic concepts of modern Riemannian geometry using the example of differential geometry of surfaces. The presentation is built on numerous concrete examples illustrating geometric ideas. It will be useful both for students and graduate students of physical and mathematical specialties, and for scientists who want to get acquainted with the basic ideas of differential geometry.