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Synopsis In the present volume the author comes to the discussion of one of the central subjects of modern pure mathematics, an understanding of which is essential also to engineers and physicists--the theory of functions of a complex variable. Author approach is classical and for that reason is an excellent introduction for those students who will go on to study the more modern developments of the theory of functions while at the same time presenting a complete picture of those aspects of the theory (conformal mappings, differential equations in the complex plane, calculus of residues) which are of most direct interest to applied mathematicians. An interesting feature of the book is that it was the first textbook at this level to include a chapter on the theory of functions of several complex variables, a subject which forms an essential tool to workers in quantum field theory.