Theory of the Quark-Gluon Plasma

These lectures are an introduction to recent developments in the study of the high temperature phase of QCD by using weak coupling techniques. After a brief introduction to some techniques of quantum field theory at finite temperature, I proceed to an analysis of the various important scales and degrees of freedom of the quark-gluon plasma and focus on the effective theory for the collective modes which develop at the particular momentum scale $gT$, where $g$ is the gauge coupling and $T$ the temperature. A powerful technique to construct the effective theory is based on kinetic equations which govern the dynamics of the hard degrees of freedom. Some of the collective phenomena that are described by this effective theory are briefly mentioned. Then I turn to the calculation of the entropy of the quark-gluon plasma and show how the information coded in the effective theory can be exploited in (approximately) self-consistent calculations.