This book starts with basic fundamental definitions of Complex Numbers and then concepts of elementary functions, complex integration, power series, convergence and uniform convergence, singularities, residues, contour integration, conformal mappings, bilinear transformations, etc. are discussed. The concepts of limit, continuity and differentiability of complex functions are also explained in detail with good examples. This book aims at helping students to get an insight of the complex functions of complex variables and will also enable them to solve the problems by an easy and effective approach. The practice sets are also introduced which includes a variety of questions from CSIR UGC NET, NBHM, and GATE previous year question Papers. The questions are carefully keeping in mind the objective of qualifying the above mentioned national level competitive exams and interviews.