Algebra of complex numbers. Polar representation. Analyticity. Cauchy- Riemann equations. Power series. Elementary functions. Mapping by elementary functions. Linear fractional transformations. Line integral. Cauchy-Theorem. Cauchy integral formula. Taylor's Series. Laurent series. Residues, Residue theorem. Improper integrals. Conformal mapping. Integral formulas of the Poisson type. The Schwarz-Christoffel Transformation.