This volume has consistently been a leading text in its field since its initial release. It has remained in continuous print, reflecting its enduring relevance and significance in scholarly and professional discourse.

One of the most widely used texts in its field, this volume has been continuously in print since its initial 1976 publication. Many examples and exercises, some with hints and answers, enhance the clear, well-written exposition. Prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables.

Comprehensive Coverage: The volume introduces a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. It provides a thorough understanding of key concepts and techniques.
Clear Exposition: The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details.
Examples and Exercises: The book includes numerous examples and exercises that enhance the learning experience. These practical applications solidify understanding and provide opportunities for practice and self-assessment.
Hints and Answers: Hints and answers to selected problems are provided, allowing readers to check their work and gain further insights into the subject matter.
Updated Edition: This second edition has been corrected, revised, and updated by the author, ensuring that the content remains current and relevant.
Suitable for Advanced Study: While suitable for advanced undergraduates, this text is also appropriate for graduate students of mathematics. Prerequisites include an undergraduate course in linear algebra and some familiarity with calculus of several variables.

About the author: Manfredo P. do Carmo was a Brazilian mathematician and authority in the very active field of differential geometry. He was an emeritus researcher at Rio's National Institute for Pure and Applied Mathematics and the author of Differential Forms and Applications.

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