Catalan's conjecture

1. Introduction

2. The Case "q = 2"

3. The Case "p = 2"

4. The Nontrivial Solution

5. Runge's Method

6. Cassels' theorem

7. An Obstruction Group

8. Small p or q

9. The Stickelberger Ideal

10. The Double Wieferich Criterion

11. The Minus Argument

12. The Plus Argument I

13. Semisimple Group Rings

14. The Plus Argument II

15. The Density Theorem

16. Thaine's Theorem

Appendix. Euler's Theorem

Index