PUB - Publikationen an der Universität Bielefeld

This paper is a slightly modified version of the introductory part of adoctoral dissertation that contained also three original articles,hep-ph/0212283, hep-ph/0305183 and hep-ph/0311323. Our purpose is to review thehistory and present status of finite-temperature perturbation theory as appliedto the context of determining the equilibrium properties of quark-gluon plasma,most notably the pressure of QCD at finite temperatures and quark chemicalpotentials. We first introduce the general formalism of finite-temperaturefield theory and perturbation theory, then follow through the evaluation of thepressure order by order, and finally proceed to analyze the most recent, orderg^6ln(g) results by comparing the perturbative predictions with lattice data.In the appendix we provide a somewhat pedagogical introduction to the mostimportant computational techniques used in the perturbative framework, namelythe analytic evaluation of multi-loop vacuum diagrams both in full QCD and inits three-dimensional high-T effective theories.