We will discuss two different approaches to describing a continuous medium (gases, liquids): the microscopic one, where we study the molecular
interactions and describe the behaviour in terms of the Boltzmann equation, and the macroscopic one, where we describe the continuous medium
by usual hydrodynamic equations, such as Euler equations or Navier-Stokes equations. We will also discuss the formal derivation of macroscopic equations from microscopic ones.

As an illustration we will take the Boltzmann equation for Fermi-Dirac statistics and briefly outline the methods of obtaining hydrodynamic equations.

Mots clés: kinetic equations, fluid dynamics, Boltzmann equation, Euler Equations, Navier-Stokes equations, entropy, Chapman-Enskog expansion.