Abstract: Pioneer works in formal deformation theory goes back to the late 60's, where a noncommutative space from a classical algebra of smooth functions was constructed. In his '98 paper Kontsevich proved the existence of a deformation called star products, on $C^\infty(M)$ where the product is understood to be a formal power series in one variable, on a Poisson manifold. In this talk I will define and derive an explicit formula on $\mathbb{R}^n$ of the star product. Furthermore I will explain Kontsevich's proof inasmuch elementary words as possible.