Elementary Differential Geometry (Springer Undergraduate Mathematics Series)

Elementary Differential Geometry by A.N. Pressley is a comprehensive resource published by Springer on March 18, 2010. This second edition spans 486 pages and is presented in English, making it accessible for students and educators alike. The book covers essential results in the differential geometry of curves and surfaces, tailored for those embarking on their first course in the subject. It maintains minimal prerequisites, requiring only foundational knowledge in linear algebra and multivariable calculus, and employs a direct approach throughout.

Readers will find a thorough exploration of key topics, including parallel transport, map coloring, holonomy, and Gaussian curvature. The revised edition introduces a chapter on non-Euclidean geometry, highlighting its significance in both historical and contemporary mathematical contexts. Additionally, the book features around 200 new exercises and provides a full solutions manual for instructors, enhancing its utility as a teaching tool. This edition aims to facilitate a clear understanding of differential geometry while ensuring that the main results can be reached efficiently through previously established techniques.