In this talk, I will introduce two types of particle Systems, an ergodic - the Simple Exclusion Process and a non-ergodic: a particle system with degenerate rates. 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 we will get to the heat equation while in the Asymmetric case to the Burgers equation and for the non-ergodic particle system we will get to the porous medium equation. I will explain the difficulties that arise when showing the hydrodynamic limit for this non-ergodic particle system.