We review different aspects of field theory at finite temperature, related to the theory of phase transitions. Finite temperature field theory is discussed in the real and imaginary time formalisms, showing their equivalence in simple examples. Bubble nucleation by thermal tunneling, and the subsequent development of the phase transition is described in some detail. Finally the application to baryogenesis at the electroweak phase transition is done in the Standard Model. We have translated the condition of not washing out any previously generated baryon asymmetry by upper bounds on the Higgs mass.

PACS numbers: 11.10.Wx, 05.70.Fh, 03.65.Xp, 64.60.Bd