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The main purpose of this second edition is essentially the same as the first edition with changes noted below. Accordingly, first we quote from the preface by Murray R. Spiegel in the first edition of this text. The theory of functions of a complex variable, also called for brevity complex variables or complex analysis, is one of the beautiful as well as useful branches of mathematics. Although originating in an atmosphere of mystery, suspicion and distrust, as evidenced by the terms imaginary and complex present in the literature, it was finally placed on a sound foundation in the 19th century through the efforts of Cauchy, Riemann, Weierstrass, Gauss, and other great mathematicians. This book is designed for use as a supplement to all current standards texts or as a textbook for a formal course in complex variable theory and applications. It should also be of considerable value to those taking courses in mathematics, physics, aerodynamics, elasticity, and many other fields of science and engineering. Each chapter begins with a clear statement of pertinent definitions, principles and theorems together with illustrative and other descriptive material. This is followed by graded sets of solved and supplementary problems. Numerous proofs of theorems and derivations of formulas are included among the solved problems. The large number of supplementary problems with answers serve as complete review of the material of each chapter. Topics covered include the algebra and geometry of complex numbers, complex differential and integral calculus, infinite series including Taylor and Laurent series, the theory of residues with applications to the evaluation of integrals and series, and conformal mapping with applications drawn from various fields. Considerable more material has been included here than can be covered in most first courses. This has been done to make the book more flexible, to provide a more useful book of reference and to stimulate further interest in the topics. Some of the changes we have made to the first edition are as follows: (a) We have expanded and corrected many of the sections to make it more accessible for our readers. (b) We have reformatted the text, such as, the chapter number is now included in the label of all sections, examples, and problems