  A brief summary of the formulation of QCD at finite chemical potental, $\mu$,
is presented. The failure of the quenched approximation to the problem is
reviewed.
  Results are presented for dynamical simulations of the theory at strong and
intermediate couplings. We find that the problems associated with the quenched
theory persist: the onset of non-zero quark number does seem to occur at a
chemical potential $\approx { {m_{\pi}} \over 2}$. However analysis of the
Lee-Yang zeros of the grand canonical partition function in the complex
fugacity plane, ($e^{\mu/T}$), does show signals of critical behaviour in the
expected region of chemical potential.
  Results are presented for a simulation at finite density of the Gross-Neveu
model on a $16^3$ lattice near to the chiral limit. Contrary to our simulations
of QCD no pathologies were found when $\mu$ passed through the value
$m_{\pi}/2}$.

High Energy Physics - Lattice