Contents: Preface. 1. Complex numbers. 2. Sequence and series. 3. Complex differentiation. 4. Elementary transcendental functions. 5. Complex integration. 6. Linear fractional transformations. 7. Calculus of residues. 8. Some relevant theorems. 9. Entire and meromorphic functions. 10. Analytic continuation. Bibliography. Index. This book is a comprehensive resource for students of undergraduate postgraduate courses in mathematics, physics and engineering. It makes use of numerous worked-out examples to show how the study of complex numbers and their derivatives and properties helps in solving many physical problems. Beginning with the algebraic and analytic properties of complex numbers, the reader is introduced to topological notions of sets in the complex plane, sequence and series representation of complex numbers, limit, continuity and differentiability of complex functions, and branch cut and branch points in multi-valued functions. Important theorems such as Ascoli–Arzela theorem, Montel’s theorem, Riemann mapping theorem, and the concept of Schawarz–Cristoffel transformations widely used in various fields are established. The notion of entire functions and their properties and direct and indirect analytic continuation of an analytic function, too, are covered. The book contains an interesting range of chapter-end review exercises that will be of help to students and teachers alike. The inclusion of multiple-choice questions, in particular, will be of interest to those preparing for competitive examinations such as the NET, SET and GATE.