This paper is a slightly modified version of the introductory part of a
doctoral dissertation that contained also three original articles,
hep-ph/0212283, hep-ph/0305183 and hep-ph/0311323. Our purpose is to review the
history and present status of finite-temperature perturbation theory as applied
to the context of determining the equilibrium properties of quark-gluon plasma,
most notably the pressure of QCD at finite temperatures and quark chemical
potentials. We first introduce the general formalism of finite-temperature
field theory and perturbation theory, then follow through the evaluation of the
pressure order by order, and finally proceed to analyze the most recent, order
g^6ln(g) results by comparing the perturbative predictions with lattice data.
In the appendix we provide a somewhat pedagogical introduction to the most
important computational techniques used in the perturbative framework, namely
the analytic evaluation of multi-loop vacuum diagrams both in full QCD and in
its three-dimensional high-T effective theories.Comment: 65 pages, 21 figures; introductory part of a PhD thesi
