Complex Analysis Book

Question

I want a really good book on Complex Analysis, for a good understanding of theory. There are many complex variable books that are only a list of identities and integrals and I hate it. For example, I found Munkres to be a very good book for learning topology, and "Curso de Análise vol I" by Elon Lages Lima is the best Real Analysis book (and the best math book) that I have read with many examples, good theory and challenging exercises.

An intuitive and introductory approach is not very important if the book has good explanations and has correct proofs.

Added: If it is possible, tell me your experience with your recommended books and if you got a really good understanding of complex analysis with a deep reading.

Answer 1

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

Answer 2

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.

Answer 3

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.

Answer 4

The books below are excellent:

• Invitation to Complex Analysis by Ralph P. Boas (second edition revised by Harold P. Boas).

• Complex Made Simple by David C. Ullrich.

Answer 5

I had really good luck with Fisher's Complex Variables and Gamelin's Complex Analysis.

Answer 6

A very classic book to learn complex analysis from is Ahlfors's book (which I used). There is also Stein and Shakarchi's book, and Bak and Newman's book.

Answer 7

Here's one that I love: Donald Sarason's book, Complex Function Theory. It's beautifully and economically written, so that it really flows. It was published by Henry Helson in his garage for a long time, but has been taken over by the American Math. Soc.

It covers complex analysis up to and including some advanced topics such as the Riemann mapping theorem, starting from basic real analysis.