  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.
