This paper gives a sketch of proof of Mazur's Theorem classifying the possible rational torsion subgroups of elliptic curves defined over rational numbers. We will prove Mazur's theorem by using two main lemmas. The sketch of proof of these two lemmas will be the goal of all the work. We will provide the tools needed to understand the proofs, trying to make the work as self-contained as possible although we must avoid some technical parts. We will present the basic notions of the theory of elliptic curves, discuss about Weierstrass equations, the Mordell-Weil group, isogenies, endomorphisms, the basics of the theory of group schemes, Néron models for elliptic curves, and modular curves.