Abstract: In this talk I will introduce a classical example of Particle System: the Simple Exclusion Process. I will give the notion of hydrodynamic limit, which is a Law of Large Numbers for the empirical measure, and I will explain how to derive from the microscopic dynamics between particles a partial differential equation describing the evolution of the density profile. For the Simple Exclusion Process, in the symmetric case ($p = 1/2$) we will get to the heat equation, while in the asymmetric case ($p \not= 1/2$) to the Burgers equation. Finally, I will introduce the Central Limit theorem for the empirical measure, and the limiting process turns out to be a solution of a stochastic partial differential equation.