  In these notes we review some properties of Statistical Quantum Field Theory
at equilibrium, i.e Quantum Field Theory at finite temperature. We explain the
relation between finite temperature quantum field theory in (d,1) dimensions
and statistical classical field theory in d+1 dimensions. This identification
allows to analyze the finite temperature QFT in terms of the renormalization
group and the theory of finite size effects of the classical theory. We discuss
in particular the limit of high temperature (HT) or the situation of finite
temperature phase transitions. There the concept of dimensional reduction plays
an essential role. Dimensional reduction in some sense reflects the known
property that quantum effects are not important at high temperature. We
illustrate these ideas with several standard examples, phi^4 field theory, the
non-linear sigma model and the Gross-Neveu model, gauge theories. We construct
the corresponding effective reduced theories at one-loop order, using the
technique of mode expansion of fields in the imaginary time variable. In models
where the field is a vector with N components, the large N expansion provides
another specially convenient tool to study dimensional reduction.
