The equation of state relates the pressure, temperature and volume of a system. Since the volume of a system is summed over those of the constituting phases, we will restrict ourselves in this chapter to phases with a fixed composition. We will begin with ideal gases which constitute a good starting point for real gases at low pressure and high temperatures. These will also allow Carnot cycles to be introduced in a simple way as entropy pumps. Then we will describe the main drawbacks of the ideal gas equation of state and, with special attention to the existence of the critical point and to gasliquid phase equilibria, the manner in which these flaws are corrected by empirical expressions such as the van der Waals equation. Condensed phases will be eventually considered. After a brief presentation of equations of state that can be used up to the highest pressures experimentally accessible, we will discuss the relationship between thermal convection and adiabatic gradient.