Complex Number and the Complex Plane; Functions of Complex Variable; Analytics Functions; Elementary Functions; Complex Integration; Cauchy's Integra Formulas and their Consequences; Analytic Functions in a Disc; Simply Connected Region; Isolated Singularities; The Calculus of Residues; Contour Integration and Summation of Series; Conformal Mapings; Schwarz's Lemma- An Automorphism of Disc.