Principal Congruence Subgroup of Level 2

This lecture delves into the study of the principal congruence subgroup of level 2, denoted as Gamma(2), focusing on establishing basic results on the group structure and computing a fundamental domain of the action of Gamma(2) on the upper half-plane. The slides present theorems related to the free generation of Gamma(2) by specific elements, the fundamental domain of its action, and the proof steps involving free groups and injectivity considerations. The lecture concludes with claims and proofs related to the injectivity of certain mappings, emphasizing the importance of understanding the structure and properties of Gamma(2).