Summary and Info
If possible, I would give this book 4.5 starts, just because I don't think it is quite as good as the great classic by Conway, "Functions of One Complex Variable" (which treats all the standard topics). On the other hand, Stein and Shakarchi's book is beautiful, lucid, and obviously written by one of the grandmaster analysts of our time. Also, I give it five stars for including a beautiful treatment of the Paley-Wiener theorem, a topic that doesn't usually make its way into elementary complex analysis texts. Finally, this book has the best treatment I've seen of the Hadamard factorization theorem.