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.
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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