Riemannian Geometry: A Beginners Guide, Second Edition

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 works in minimal surfaces and studies the behavior and structure of minimizers in various dimensions and settings. His proof with colleagues and students of the Double Bubble Connecture is featured at the NSF Discoveries site. Morgan served at Williams as Mathematics Department Chair and founding director of an NSF undergraduate research project. He is currently Webster Atwell '21 Professor of Mathematics at Williams College. He is the author of six books.