Chapters in this book

1. Frontmatter i
2. Contents vii
3. Preface xi
4. PART 1. General theory of curves
5. Chapter One. Fundamental ideas 3
6. Chapter Two. Elimination theory 21
7. Chapter Three. Singular points and intersections 37
8. Chapter Four. Branches and parametrisation 63
9. Chapter Five. The function field of a curve 110
10. Chapter Six. Linear series and the Riemann–Roch Theorem 161
11. Chapter Seven. Algebraic curves in higher-dimensional spaces 199
12. PART 2. Curves over a finite field
13. Chapter Eight. Rational points and places over a finite field 277
14. Chapter Nine. Zeta functions and curves with many rational points 332
15. PART 3. Further developments
16. Chapter Ten. Maximal and optimal curves 395
17. Chapter Eleven. Automorphisms of an algebraic curve 458
18. Chapter Twelve. Some families of algebraic curves 546
19. Chapter Thirteen. Applications: codes and arcs 590
20. Appendix A. Background on field theory and group theory 627
21. Appendix B. Notation 650
22. Bibliography 655
23. Index 689