In this chapter, the authors begin by developing the partition function and the effective potential for the gauge field theories at finite temperature before applying these methods to the Higgs model, as a warm-up, and then to electroweak theory and grand unified theory. In each case, the nature of the phase transitions that occur as the temperature of the universe drops is studied. The authors then extend the discussion to gauge theories with global supersymmetry and local supersymmetry (supergravity). Finally, the nucleation of (stable) ‘true’ vacuum from (metastable) ‘false’ vacuum in first-order phase transitions is considered. This nucleation rate will control the extent of any supercooling that occurs before the phase transition is complete.