In this chapter, we move on to the so-called macroscopic descriptionMacroscopic descriptionFluid description (also called fluid description) of plasmas, which contains less information than the kinetic formulation. Knowledge of a distribution function f provides us with statistical information in the \(\textbf{r},\textbf{p}\) phase space at any given time t. (Here, we do not address the difference between descriptions using \(\textbf{p}\) or \(\textbf{v}\) , as previously mentioned.) If we are not interested in the details in velocity space, we can integrate over the velocities to obtain equations for the so-called momentsMoment of the distribution function. Of course, a finite number of moments mathematically contains less information than the distribution function itself. We should mention that the physical consequences of the reduced, macroscopic description also depend on the time and spatial variables. We assume that the moments vary (slowly) on the so-called hydrodynamic time and length scales, which generally differ from the characteristic microscopic variations. We will develop the macroscopic theory for plasmas in the following sections. First, we define the moments. When we attempt to derive the equations for the moments, we encounter a hierarchy problem, similar to the difficulties in deriving a (closed) kinetic equation. To illustrate the steps necessary to obtain a closed system of equations for the first three moments, we will, for pedagogical reasons, first summarize the steps known from the theory of neutral gases. In doing so, we will not present all the details of the calculations, as these will appear later when we develop the plasma counterpart.