This text emphasizes the special functions that are used in complex analysis. Starting with the algebraic system of complex numbers, it offers an entry-level course on complex analysis of one variable. It presents the study of analytic functions, conformal mapping, analysis of singularities, and the computation of various integrals. The final three chapters introduce more advanced topics and applications. The book provides examples of applications to various physical problems and explains how to use Mathematica (R), Maple (TM), and MATLAB (R).