This book‎,‎ divided in ten chapters deals with‎:‎ algebra of complex numbers and its various geometrical properties‎,‎ properties of polar form of complex numbers and regions in the complex plane‎;‎ limit‎,‎ continuity‎,‎ differentiability‎;‎ different kinds of complex valued functions‎;‎ different types of transformations‎;‎ conformal mappings of different functions‎;‎ properties of bilinear and special bilinear transformation‎;‎ line integrals‎,‎ their properties and different theorems‎;‎ sequences and series‎,‎ Power series‎,‎ Zero‎'‎s of functions‎,‎ residues and residue theorem‎,‎ meromorphic functions‎,‎ different kinds of singularities‎;‎ evaluation of real integrals‎;‎ analytic continuation‎,‎ construction of harmonic functions‎,‎ infinite product‎,‎ their properties and Gamma function‎;‎ Schwarz‎-Christoffel transformations‎,‎ mapping by multi valued functions‎,‎ entire functions‎;‎ and‎,‎ Jenson‎'‎s theorem and Poisson‎-Jenson theorem‎.‎ The book is designed as a textbook for UG and PG students of science as well as engineering‎.‎