Preface
Chapter 1. Introduction: A Metamathematical View of Differential Geometry
1. Algebra and Geometry - the Duality of the Intellect
2. Two Examples: Algebraic Geometry, Propositional Logic and Set Theory
3. On the History of Geometry
4. Differential Calculus and Commutative Algebra
5. What is Differential Geometry?
Chapter 2. The Geometry of Surfaces
Chapter 3. The Field Approach of Riemann
Chapter 4. The Group Approach of Lie and Klein. The Geometry of Transformation Groups
Chapter 5. The Geometry of Differential Equations
Chapter 6. Geometric Structures
Chapter 7. The Equivalence Problem, Differential Invariants and Pseudogroups
Chapter 8. Global Aspects of Differential Geometry
Commentary on the References
References
Author Index
Subject Index