Finite temperature field theory

This paper is a pedagogical review for non-experts of some topics in finite temperature quantum field theory. It begins with a review of thermodynamics and a summary of the lattice results for phase transitions in the electroweak and QCD theories. The main topic is the perturbative computation of thermal Green functions and the five standard formulations in imaginary time and real time. A summary of nonrelativistic plasma physics emphasizes the TEM and longitudinal waves. The last section reviews chirally-invariant gauge theories at high temperature, which have the same modes of oscillation. It demonstrates in simple situations the breakdown of perturbation theory and the Braaten-Pisarski resummation program that solves it