This chapter introduces the fundamental concepts of finite temperature perturbation theory by first exploring the properties of a quantum harmonic oscillator at finite temperature, particularly deriving its partition function using both the energy basis and the Euclidean path integral formalism. This groundwork is then extended to the partition function for a free scalar field theory, where the concepts of imaginary time, Matsubara frequencies, and sum-integrals are developed and applied to calculate the free energy density and thermodynamics. The discussion concludes by introducing the interacting scalar \(\phi ^4\) theory to illustrate the challenges of perturbation theory at finite temperature, specifically the appearance of infrared divergences. This leads to an overview of modern resummation methods, such as Hard Thermal Loops and Screened Perturbation Theory, which are necessary for reliable calculations of quantities like the pressure and for understanding high-temperature matter like the Quark-Gluon Plasma.