i second tristan needham's visual complex analysis. some other good ones: * the one we used in my undergrad course was fisher's complex variables which is gre

i second tristan needham's visual complex analysis. some other good ones: * the one we used in my undergrad course was fisher's complex variables which is great if you're learning for the purposes of applications. it's a cheap dover book. * rudin's real and complex analysis (if theory is your thing. note that rudin's books, while great, do require a good background in math). * as the article mentions, eli stein has a series of books on the four main branches of analysis. i believe the second book is on complex analysis.