Reading List

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There is a number of books that cover many of these topic. I would suggest

1. L. Ahlfors, Complex analysis. This is a very good advanced textbook on Complex analysis. If you are a bit rusty on the basic complex analysis, then you might find everything you need (and a bit more) in Chapters 1-4. We will cover some of the material from chapters 5-6.
2. L. Ahlfors, Conformal Invariants. We will cover some topics from Chapters 1-6.
3. Ch. Pommerenke, Univalent functions. This book is mostly for further reading. We will discuss some of the results that are covered in Chapters 1,5,6, and 10.
4. Ch. Pommerenke, Boundary behaviour of conformal maps. This is an updated version of the previous book. We will be interested in Chapters 1,4, and 8.
5. P. Duren, Univalent functions. This is an excellent book about general theory of the univalent functions. We are mostly interested in the first three chapters.
6. G. Goluzin, Geometric Theory of Functions of a Complex Variable. This book contains vast amount of information about the geometric function theory. We will cover some of the results from the first four chapters.