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This is a very successful textbook for undergraduate students of pure mathematics. Students often find the subject of complex analysis very difficult. Here the authors, who are experienced and well-kwn expositors, avoid many of such difficulties by using two principles: (1) generalising concepts familiar from real analysis; (2) adopting an approach which exhibits and makes use of the rich geometrical structure of the subject. An opening chapter provides a brief history of complex analysis which sets it in context and provides motivation.