This book, an introduction to basic Complex Analysis at the undergraduate and postgraduate levels, features an integrated approach to the concept of differentiation for complex valued functions of a complex variable, unified Cauchy Riemann equations, a detailed discussion on the construction of Riemann surfaces for elementary functions leading to its abstract concept, step-by-step development of the most general form of Cauchy’s theorem, complex version of the real intermediate value theorem, exhaustive treatment of contour integration and an introduction to the theory of univalent functions on the unit disc including a brief history of the Bieberbach’s conjecture and its solution. New to the Second Edition: Complete section on Analytic automorphisms on plane domains

• • Solved Problems • Historical Remarks • Suggestion for further reading

Preface to the Second Edition / Preface to the First Edition / A Bird's eye view of the complex plane / Elementary Properties of Analytic Functions / Conformal Mappings / Complex Integral Calculus / Riemann Mapping Theorem / Solved Exercises / Index.

Undergraduate and Postgraduate Students