This book weaves together theory and extensive applications in mathematics, physics and engineering. In this edition there are many new problems, revised sections, and an entirely new chapter on analytic continuation. There is excellent coverage of topics such as series, residues and the evaluation of integrals, multi-valued functions, conformal mapping, dispersion relations and analytic continuation. The presentation is systematic and clear, with many diagrams to clarify discussion of the material. This work will serve as a textbook for undergraduate and graduate students in the areas noted above.