1.The complex number system. 2.Metric spaces and the topology of C. 3.Elementary properties and examples of analysis functions. 4.Complex integration. 5.Singularities. 6.The maximum modules theorem. 7.Compactness and convergence in the space of analysis functions. 8.Runge’s theorem. 9.Analytic continuation and Riemann surfaces. 10.Harmonic functions. 11.Entire functions. 12.The range of an analytic functions.