Part I The Intuitive Background
1. Mathematical Thinking
2. Number Systems
Part II The Beginning of Formalization
3. Sets
4. Relations
5. Functions
6. Mathematical Logic
7. Mathematical Proof
Part III The Development of Axiomatic Systems
8. Natural Numbers and Proof by Induction
9. Real Numbers
10. Real Numbers as a Complete Ordered Field
11. Complex Numbers and Beyond
Part IV Using Axiomatic Systems
12. Axiomatic Systems, Structure Theorems, and Flexible Thinking
13. Permutations and Groups
14. Cardinal Numbers
15. Infinitesimals
Part V Strengthening the Foundations
16. Axioms for Set Theory