Lattice Regularized QCD at Finite Temperature

During the first part of this review we will focus on the thermodynamics of $SU(N)$ gauge theories at finite temperature. We will present results from a calculation of electric and magnetic screening masses for the gluons, discuss calculations of the critical temperature in units of the string tension and bulk thermodynamic quantities like the energy density and pressure. In particular, the latter calculations have now reached a stage where $O(a^2)$ cut-off effects can be controlled systematically and an extrapolation to the continuum limit can be performed. In the second part we discuss the critical behaviour of QCD with light quarks. We analyze the chiral transition in 2-flavour QCD and present results on the temperature dependence of hadron properties.