This classic text serves as a tool for self-study; it is also used as a basic text for undergraduate courses in differential geometry. The author's ability to extract the essential elements of the theory in a lucid and concise fashion allows the student easy access to the material and enables the instructor to add emphasis and cover special topics. The extraordinary wealth of examples within the exercises and the new material, ranging from isoperimetric problems to comments on Einstein's original paper on relativity theory, enhance this new edition.
Frank Morgan is the Atwell Professor of Mathematics at Williams College in Williamstown, Massachusetts.
… an intuitive approach to Riemannian geometry based on surfaces in n-dimensional Euclidean spaces. … This revision of the second edition includes many interesting exercises and solutions to selected exercises. … The book is warmly recommended to specialists in mathematics, physicists and especially to PhD students interested in this topic.
—Jan Kurek, Zentralblatt MATH 1234