This is a mathematical text suitable for students of graduate and post-graduate level or beyond. It is an encyclopaedia of applicable mathematics. It avoids of approach of listing only the techniques, followed by a examples. Equally, the text has been written as an encyclopaedia mathematics with a list applications. On the whole, the authors have been generous in writing down all the steps in solving the example problems. Each chapter of this encyclopaedia in two volumes contains several solved problems clarifying the introduce concepts. Some of the examples are serve to illustrate the applications in various fields of engineering and science. At the end of each chapter, there are assignment problems. This encyclopaedia is the product of a close collaboration between mathematicians and an engineer. This encyclopaedia is a rigorous introduction to the subject of complex analysis. The author have made an effort to present some of the deeper and more interesting results, for example, Taylor’s theorems, Riemann mapping theorem, Schwarz lemma in few chapters. However, the very basic theory is nevertheless given a through treatment so that readers should never feel lost. Each chapter finishes with exercises.