| ÖÇ1 | Learns the concepts of fundamental spaces, the hyperbolic plane model, the Riemann sphere and the boundary at infinity of the upper half-plane. |
| ÖÇ2 | Learns concepts of Group of Möbiüs Transformations,Transitivity Properties and Cross Ratio |
| ÖÇ3 | Learns how to classify of Möbiüs Transformations and Matrix Representation |
| ÖÇ4 | Learns the concepts of conformality of Möbiüs Transformations and preserving of upper half-plane |
| ÖÇ5 | Learns the concepts of Topological groups, Topological transformation groups and the group PSL(2,IR) |
| ÖÇ6 | Learns the concepts of hyperbolic distance, hyperbolic length and hyperbolic area in upper half-plane and Gauss-Bonnet Formula |
| ÖÇ7 | Learns the concepts of Fuchsian groups and fundamental region concepts |