A thoroughly revised Complex Variables and Applications, in its Ninth Edition, still preserves the basic content and style of the earlier editions and continues to be a popular textbook on introductory course in the theory and application of functions of a complex variable. The text is designed to develop those parts of the theory that are prominent in applications of the subject and also to furnish an introduction to applications of residues and conformal mapping. To accommodate the different calculus backgrounds of students, footnotes are given with references to other texts that contain proofs and discussions of the more delicate results from calculus and advanced calculus. Improvements in the text include extended explanations of theorems, greater detail in arguments, many new examples and the separation of topics into their own sections. Salient Features: 1) The treatment of the extended form of the Cauchy integral formula for derivatives has been completely rewritten, with special attention to its immediate consequences. 2) Improvements include more details in arguments involving mathematical induction, greater emphasis on rules for using complex exponents, some discussion of residues at infinity, and a clearer exposition of real improper integrals and their Cauchy principal values. 3) Important material is presented in a more focused way by placing it in separate sections. For instance, the discussion of upper bounds of moduli of contour integrals is now entirely in one section, and there is a separate section devoted to the definition of isolated singular points.