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Ahlfors has been the standard text for complex function theory for quite some time. I like it, but he's very classical and concrete in outlook: nary a function space or a norm in the whole book. The exposition is a classic, though. [Pete Clark] Everyone lists it; do people actually read it? I'd use Conway instead. MR 80c:30003 This book starts very, very slow and easy, so if you're rusty on metric spaces or real-variable theory you have no need to worry. Conway's style is to prove things very thoroughly, but relegate the occasional proof to the exercises. The text is more modern than Ahlfors; Conway proves Runge's theorem using Banach space techniques (well, he's an operator theorist). I like the book more for this reason, but I finally sold my copy because the slow pace got to me. [Pete Clark] I like the book, but I hear your criticisms. The chapter on convergence in the compact-open topology, arguably the most important topic in the whole book, is marred by the fact that he mixes met

Intermediate - Complex analysis Ahlfors, Complex analysis MR 80c:30001 Ahlfors has been the standard text for complex function theory for quite some time. I like it, but he's very classical and concrete in outlook: nary a function space or a norm in the whole book. The exposition is a classic, though. [Pete Clark] Everyone lists it; do people actually read it? I'd use Conway instead. Conway, Functions of one complex variable I MR 80c:30003 This book starts very, very slow and easy, so if you're rusty on metric spaces or real-variable theory you have no need to worry. Conway's style is to prove

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