A standard source of information of functions of one complex variable,
this text has retained its wide popularity in this field by being
consistently rigorous without becoming needlessly concerned with
advanced or overspecialized material. Difficult points have been
clarified, the book has been reviewed for accuracy, and notations and
terminology have been modernized. Chapter 2, Complex Functions, features
a brief section on the change of length and area under conformal
mapping, and much of Chapter 8, Global-Analytic Functions, has been
rewritten in order to introduce readers to the terminology of germs and
sheaves while still emphasizing that classical concepts are the backbone
of the theory. Chapter 4, Complex Integration, now includes a new and
simpler proof of the general form of Cauchy's theorem. There is a short
section on the Riemann zeta function, showing the use of residues in a
more exciting situation than in the computation of definite integrals.

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