In this volume of the Encyclopaedia, the authors give a tour of the principal areas and methods of modern differential geometry. Some topics, though important, have not previously appeared in books with a general readership. The book is structured to allow the reader to skip about the text, rather than systematically reading from beginning to end. Compared to other EMS volumes, EMS 28 has an increased appeal for early graduate students.

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This book provides a tour of the principal areas and methods of modern differential geometry. Beginning at the introductory level with curves in Euclidian space, the sections become more challenging, arriving finally at the advanced topics that form the greatest part of the book: transformation groups, the geometry of differential equations, geometric structures, the equivalence problem, the geometry of elliptic operators.

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