Complex Analysis Book

My biggest recommendation is Tristan Needham's Visual Complex Analysis. Although not a strict textbook, all of the traditional theorems in elementary complex analysis are covered. Proofs aren't thorough, but are instead explained geometrically in general outlines. The big advantage with this book is the massive amount of pictures, nearly on every page in some sections.

Other great classics are Rudin's Real and Complex Analysis, Conway's Functions of One Complex Variable. For a thorough but relatively intuitive approach, I also heavily recommend Sarason's Complex Function Theory.

Conway, "Functions of One Complex Variable I" http://books.google.ca/books?id=9LtfZr1snG0C

The followings are very, very good. Note that you should start with the first one if you are a beginner.

• Reinhold Remmert. Theory of complex functions. Springer 1991.
• Reinhold Remmert. Classical topics in complex function theory. Springer 2010.