Thermal field theory and the QCD Equation of State

This Chapter introduces QCD at finite temperature and density. We first present the formulation of the thermal theory in the Euclidean path integral formalism. We then describe how the strong dynamics at high temperature can be inspected through thermal effective field theories. As a concrete example of thermodynamic quantity, we discuss the Equation of State, which characterises the equilibrium properties of the QCD plasma. We finally conclude with an overview of the phase diagram of strongly interacting matter.