This work tries to understand the Poincaré conjecture statement and some of the tools that were used and developed towards its proving. It contains a historic introduction that explains how the problem arised and when the main steps towards its solving were maid. then there is a chapter that explains previous concepts about manifolds. In the following chapter the concepts of fundamental group and covering space are defined and also some propositions, theorems and examples of this concepts are provided. Finally there is a homology chapter with the definition of this concepts and some theorems and examples. And, to end with, a descriptive chapter about further developments in the conjecture

La conjectura de Poincaré sobre la caracterització topològica de l'esfera és actualment un teorema. El treball analitzarà la conjectura i els elements principals que intervenen en la seva demostració.