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This text is a rigorous introduction on an elementary level to the theory of analytic functions of one complex variable. At American universities it is intended to be used by first-year graduate and advanced undergraduate students.
Since the time the first edition was published there has been a marked change in the quality of American students of mathematics. They enter college better prepared, and they are confronted with true mathematical reasoning at an earlier stage. To a lesser degree the same is true abroad.
In preparing the second edition the author has striven to adjust to this greater maturity of the readers. At the same time the essentially elementary character of the exposition has not been sacrificed. Indeed, nothing could be gained by addressing only the ablest students. Therefore, as in the first edition, the presentation is comparatively broad in the beginning, except for condensed reviews of familiar material, and rises only slowly to a higher level of conciseness. The author has tried to emphasize economy of thought in order to make the reader aware of the intrinsic unity which is so characteristic of the subject