From reviews of previous editions: „This is a highly recommendable textbook dealing with an introduction to differential geometry. It presents all features which are important for a useful text to be taken by a student as a background to become acquainted with the subject and to have a reference for further studies available [...]“ — Bernd Wegner, Zentralblatt für Mathematik „A terrific new book on differential geometry: a preliminary chapter eases the way from the familiar axiomatic treatment into the differential perspective. There are also very good discussions about discrete approximations to curves and surfaces, a complete proof of the existence of triangulations on surfaces, and a beautiful discussion of cartography and constant curvature geometries. Bär provides plenty of intuition and many examples, while not stinting on the rigor.“ — Rafe Mazzeo, Stanford University