[For the entire collection see Zbl 0559.00021.]
The last few years have seen increasing interest in the study of quantum field theories at nonvanishing temperature and density. To a large extent this interest comes from the desire to use modern particle theories in cosmology, especially in the attempts to understand the very early history of the universe. There are other reasons for this interest: The possible existence of superdense ”quark stars” and the widespread speculations that very energetic collisions of heavy ions might produce a fireball consisting of a quark-gluon plasma.
My own interest in the subject is more theoretically motivated: Since in my view two central phenomena of modern quantum field theory, namely confinement of quarks and the ”Higgs mechanism” are still insufficiently understood it might be enlightening to approach these problems from a different angle where one has an extra parameter - temperature - to play with.
In these lectures I first give a general discussion of the (lattice) field theoretic formalism at finite temperature and its foundations; then I describe and explain a few results, partly of a mathematical character, partly numerical, pertaining to the phase structure of lattice gauge theories at finite temperature. These results are mostly based on collaboration with various colleagues, in particular C. Borgs, F. Karsch and I. O. Stamatescu.