What a great book this is!
This is a book that any math afficionado must have, and will undoubtedly savor. I frankly don't understand those reviewers who have given this book fewer than five stars. In fact, five stars wouldn't seem to be enough here. This book is among the best math books one will ever find! What else would one want from a such book? It is exciting, friendly, creative, often funny, crystal clear, fresh, deep, and unfailingly courteous to the reader--a quality not always found in math texts.
Additionally, this book succeeds on another level -- it is just plain beautiful. Math, to be great, must be beautiful, while books about great math too often are not. This book is truly beautiful, even artful. The author has taken great care to create beauty here.
I intially bought this book, because as an ex-mathematician whose analysis skills were getting rusty I wanted to revisit complex analysis. This book certainly succeeded in brushing up those old skills, but it also deepened them. The book has marvelous insights and geometric drawings that demonstrate in a clever way the links between complex analysis and other branches of math and physics. How could one not love the lovely and intricate drawings that depict, say, loxodromic transformations on a sphere, or the eye-popping diagrams of rotations in hyperbolic space? They're fabulous! Even the problem sets are delightful.
As a side note, some of the historical glosses about mathematicians are also very lively, and are another source of pleasure here.
On the dust jacket is the blurb--"If you must buy only one math book this year, this is the one to buy." I have to agree. I bought a couple dozen math books last year, and this one outshines the rest. I can't recommend it highly enough, even if you already feel comfortable with complex analysis.
I encourage my fellow readers to pick this up, and see how beautiful a math book can be.