"Complex analysis is one of the classical branches in mathematics that deals with the study of functions of complex variables in the same way that Real Analysis deals with the study of functions of real variables. It focuses mainly on Holomorphic Functions, and on differentiation and integration of these functions. Complex analysis, in particular the theory of conformal mappings, has many physical applications and is also used throughout analytic number theory. Introduction To Complex Analysis presents state of the art in novel ideas and techniques, and developments in complex analysis and its applications for the benefit of specialists as well as a broader audience of researchers. It discusses some introductory ideas associated with complex numbers, their algebra and geometry. This includes a look at their importance in solving polynomial equations, how complex numbers add and multiply, and how they can be represented. For the past years complex analysis has contributed a significant role not only in the sciences and engineering but also in the growth of different areas of pure and applied mathematics: number theory, algebra, the theory of ordinary and partial differential equations, differential geometry, numerical analysis etc. The original research articles as well as review articles on complex numbers and functions, and their application across mathematics, science, and engineering are covered."