Elementary Differential Geometry

  • Andrew Pressley

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Andrew Pressley
    Pages 1-27
  3. Andrew Pressley
    Pages 29-54
  4. Andrew Pressley
    Pages 55-65
  5. Andrew Pressley
    Pages 67-93
  6. Andrew Pressley
    Pages 95-119
  7. Andrew Pressley
    Pages 121-157
  8. Andrew Pressley
    Pages 159-177
  9. Andrew Pressley
    Pages 179-213
  10. Andrew Pressley
    Pages 215-245
  11. Andrew Pressley
    Pages 247-268
  12. Andrew Pressley
    Pages 269-304
  13. Andrew Pressley
    Pages 305-333
  14. Andrew Pressley
    Pages 335-377
  15. Back Matter
    Pages 379-473

About this book


Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates.

Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout.

New features of this revised and expanded second edition include:

  • a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book.
  • Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature.
  • Around 200 additional exercises, and a full solutions manual for instructors, available via

Praise for the first edition:

"The text is nicely illustrated, the definitions are well-motivated and the proofs are particularly well-written and student-friendly…this book would make an excellent text for an undergraduate course, but could also well be used for a reading course, or simply read for pleasure."

Australian Mathematical Society Gazette

"Excellent figures supplement a good account, sprinkled with illustrative examples."

Times Higher Education Supplement


Curves and Surfaces Differential Geometry Euclidean Geometry Gaussian curvature Gauss–Bonnet theorem Geometry Minimal surface curvature

Authors and affiliations

  • Andrew Pressley
    • 1
  1. 1.Department of MathematicsKing’s College LondonLondonUK

Bibliographic information