Books

Ahlfors, Complex Analysis
Gamelin, Complex Analysis
Rudin, Real and Complex Analysis
Silverman, Richard. Complex Analysis with Applications
Stein and Shakarchi, Complex Analysis Link to PDF #resources/textbooks
Taylor, Complex Analysis
Barry Simon, Basic Complex Analysis
Hormander, An Introduction to Complex Analysis in Several Variables

Technically a PDEs book, but mostly analysis.
Lang, Complex Analysis

There are plenty of solution manuals.
Springer GTM, Gilman, Complex Analysis In the Spirit of Lipman Bers
Sarason, Complex Function Theory Link to PDF #resources/textbooks
Freitag
Conway