  In this thesis the finite temperature transition between confined and
deconfined matter is studied at zero and nonzero quark densities. The findings
are relevant for the understanding of the evolution of the early Universe and
contemporary and upcoming heavy ion experiments. The results were obtained
using large-scale simulations on lattices with various physical extents and
lattice spacings, at physical values of the parameters of the theory. First the
phase diagram of QCD in the chemical potential-temperature plane is determined
for small chemical potentials via a Taylor-expansion technique. Second the
equation of state is studied with 2+1 flavors of dynamical quarks. Finally, the
equation of state is calculated in pure gauge theory up to extremely high
temperatures, where a comparison to perturbation theory is carried out.
