Two Lectures On Phase Mixing

The dynamics of phase transitions plays a crucial r\^ole in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified assumptions concerning the complex mechanisms typical of nonequilibrium field theories. After reviewing well-known results concerning the dynamics of first and second order phase transitions, I argue that much is yet to be understood, in particular in situations where homogeneous nucleation theory does not apply. I present a method to deal with departures from homogeneous nucleation, and compare its efficacy with numerical simulations. Finally, I discuss the interesting problem of matching numerical simulations of stochastic field theories with continuum models.