The QCD phase diagram has been well-understood along the temperature axis,
both by analytical arguments and lattice simulations. The situation along
the chemical potential axis is a different story. Because of the phase of the 
fermion determinant Monte-Carlo simulations are not possible and first 
principle information of QCD at finite density is lacking. 
In this lecture, we will discuss the effect of the phase of the 
fermion determinant on the chiral phase transition and emphasize
the role of the spectral density of Dirac operator. Our ideas will
be illustrated by exact analytical results in the so called microscopic 
domain of QCD.