Nine Introductions in Complex Analysis - Revised Edition

The book addresses many topics not usually in "second course in complex analysis" texts. It also contains multiple proofs of several central results, and it has a minor historical perspective.

- Proof of Bieberbach conjecture (after DeBranges)
- Material on asymptotic values
- Material on Natural Boundaries
- First four chapters are comprehensive introduction to entire and metomorphic functions
- First chapter (Riemann Mapping Theorem) takes up where "first courses" usually leave off

Chapter 1: Conformal Mapping and the Riemann Mapping Theorem

Chapter 2: Picard's Theorems

Chapter 3: An Introduction to Entire Functions

Chapter 4: Introduction to Meromorphic Functions

Chapter 5: Asymptotic Values

Chapter 6: Natural Boundaries

Chapter 7: The Bieberbach Conjecture

Chapter 8: Elliptic Functions

Chapter 9: Introduction to the Riemann Zeta-Function

Appendix

Bibliography

Index