TITLE: Complex Analysis Book to follow Ahlfors.
QUESTION [5 upvotes]: I have worked through Ahfors for an introduction to Complex Analysis. I am seeking advice on the books to read to learn more Complex Analysis. At this point, one name suggested to me has been Conway. My background includes Analysis at the US undergrad level -- analysis in euclidean spaces, point set topology, measure theory, basic functional analysis and differentiable manifolds.

REPLY [2 votes]: You know, Ahlfors himself wrote such a book.  
Conformal Invariants: Topics in Geometric Function Theory
Prerequisites for the book are exactly the topics in Ahlfors's Complex Analysis