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In this thesis we introduce the notion of elliptic functions, and in particular Weierstrass' Elliptic Function, in order to define the modular function $\lambda$ on the upper half plane. We establish a group ismorphism between the unimodular transformations and $\Aut{\C\setminus\{0,1\}}$. In particular this gives two functional equations involving $\lambda$, and with these equations we show th
