Cosmological Phase Transitions *

In this lecture at a school for condensed matter physicists, I begin with basic concepts and tools for investigating phase transitions in quantum field theory. The very different roles of global and gauge symmetries in phase transitions will be elucidated. Among the important applications of the basic theory the thermodynamics of the electroweak transition is treated in detail, and the implications for baryogenesis will be discussed. The status of lattice simulations of the transition from a high temperature quark-gluon plasma to confined hadronic matter with spontaneously broken chiral symmetry is also briefly reviewed. The various changes of the free energy density in cosmological phase transitions reinforce the cosmological constant problem. In the last part of the lecture I shall address this profound mystery of present day physics.