1.Introduction. 2.Complex numbers. 3.Sets and functions, limits and continuity. 4.Sets and functions, limits and continuity-continued. 5.Infinity and stereographic projection. 6.Homeomorphisms. 7.Differentiation and the Cauchy Riemann equations. 8.Geometric interpretation of the derivative. Conformal mapping. 9.Elementary entire functions. 10.Elementary meromorphic functions. 11.Elementary multiple-Value functions. 12.Rectifiable curves, complex integrals. 13.Cauchy’s integral. Theorem. 14.Cauchy’s integral and related topics. 15.Uniforms convergence. Infinite products. 16.Power series: Rudiments. 17.Power series: Ramifications. 18.Methods for expanding functions in Taylor series.