Regular maps and the normalizer of Γ_0(N) in PSL(2,R)

In this study, it is aimed to obtain the regular maps corresponding to Γ_0(N) analytically for some values of N which makes Γ_B(N) a triangle group. For this, we first find appropriate subgroups of Γ_B(N), and then we investigate the structure of these subgroups. Therefore, we reveal the relationship between the obtained subgroups and the regular maps corresponding to Γ_0(N). The present study consists of two main chapters. In the first chapter, the basic concepts required for our study are introduced. In the second chapter, we give our results. In the results section: the structure of Γ_B(N) and its subgroups, for which values of N, 3- valent maps, 4-valent maps or 6-valent maps will be obtained, for each case, obtaining 3- valent maps, 4-valent maps and 6-valent maps analytically are given.