This course addresses several topics in complex analysis. So, it covers the following Topics: the complex numbers, Cauchy-Riemann conditions, analytic functions and their properties, special analytic functions including linear fractional transformations, roots, exponential, Logarithm, trigonometric and hyperbolic functions of a complex variable, complex integration and line integrals, Cauchy's theorem, Cauchy representation, Taylor and Laurent series expansions, the calculus of residues and various applications.