Books
[Ahlf79]
Gamelin, Complex Analysis
Rudin, Real and Complex Analysis
Richard Silverman, Complex Analysis with Applications
Taylor, Complex Analysis
Simon, Basic Complex Analysis
Hörmander, An Introduction to Complex Analysis in Several Variables
Lang, Complex Analysis
Gilman, Kra, and Rodríguez, Complex Analysis: In the Spirit of Lipman Bers
Sarason, Complex Function Theory PDF
Freitag and Busam, Complex Analysis
Conway, Functions of One Complex Variable I
UGA course notes
Jingzhi Tie, UGA Math 8150 notes on the Riemann mapping theorem (Spring 2020)
Jingzhi Tie, UGA Math 8150 notes on normal families and Montel’s theorem (Spring 2020)
Jingzhi Tie, UGA Math 8150 conformal-mapping examples (Spring 2020)
Summaries
Douglas N. Arnold, complex-analysis lecture notes (Penn State, Spring 1997)
Josh Swanson, *2013 Complex Prelim Notes* (September 6, 2013) — qualifying-exam review notes covering basic mapping theorems, Cauchy and Poisson formulas, analytic extension, root counting, approximation, normal families, harmonic and subharmonic functions, inequalities, series and products, analytic continuation, residues, and conformal maps. The notes name Marshall’s notes as their principal source, with Ahlfors, Gamelin, and Rudin also consulted.