Nine Introductions in Complex Analysis

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. It features: proof of Bieberbach conjecture (after DeBranges), material on asymptotic values and material on Natural Boundaries. The first four chapters are comprehensive introduction to entire and metomorphic functions. The first chapter (Riemann Mapping Theorem) takes up where "first courses" usually leave off.