Lattice QCD at Finite Density

Abstract

I discuss different approaches to finite density lattice QCD. In particular, I focus on the structure of the phase diagram and discuss attempts to determine the location of the critical end-point. Recent results on the transiton line as function of the chemical potential ($T_c(\mu_q)$) are reviewed. Along the transition line, hadronic fluctuations have been calculated, which can be used to characterize properties of the Quark Gluon plasma and eventually can also help to identify the location of the critical end-point in the QCD phase diagram on the lattice and in heavy ion experiments. Furthermore, I comment on the structure of the phase diagram at large $\mu_q$.Comment: Plenary talk at XXIVth International Symposium on Lattice Field Theory (Lattice 2006). Version to appear as PoS (LAT2006) 021; references adde