NB. I was sent this book as a review copy.
This is a no-nonsense, clearly written graduate level textbook on complex analysis, and while it is written for a graduate audience, I think that the way it is laid out, with clear examples throughout, a keen undergraduate with a background in analysis and topology. As such it is far more approachable than many other books on complex analysis and I would say that it would be perfectly suited for physics students wanting to go into areas like quantum field theory, particularly string theorists where the sections on conformal metrics and the modular group would be very helpful.
One thing to look out for in a book like this is the clarity of the proofs, and the number of intermediate lines which are included, and in this case I think that there is just the right amount to make everything easy to follow, but not overwhelming the material.
While the book definitely has more of a topological bent than many other similar-level textbooks on complex analysis, if I were teaching a class on this topic, using this book as a primary resource would make a lot of sense. With plenty of well thought-out exercises, nice illustrations and a sensible flow of topics, this is an excellent addition to the cannon of books on this topic and should go high up on anyone’s list if you are teaching within this area.
For a complete table of contents, see here.