1.Historical develipment. 2.Preparatory material. 3.Discontinuous groups. 4.The fundamental región. 5.Automorphic functions and forms. 6.Riemann surfaces. 7.Th estructure of discontinuous groups. 8.Forms of negative dimension. 9.Forms of positive and zero dimensions. 10.Transitivy. 11.The molecular groups and modular functions. 12.Automorphic functions of several complex variables.