p-adic uniformization of elliptic curves

This thesis studies elliptic curves on various fields to gain a deeper understanding of Tate’s p-adic uniformisation theorem. The first chapter consists of an overview on elliptic curves with their properties, for example the Group Law, and elliptic curves on the complex numbers Then, we analyse non-archimedean local fields and we study Elliptic curves defined on those. In the final chapter we state and prove the p-adic uniformisation theorem of elliptic curves.