  Phase transition from hadronic matter to quark-gluon matter is discussed for
various regimes of temperature and baryon number density. For small and medium
densities, the phase transition is accurately described in the framework of the
Field Correlation Method, whereas at high density predictions are less certain
and leave room for the phenomenological models. We study formation of
multiquark states (MQS) at zero temperature and high density. Relevant MQS
components of the nuclear matter can be described using a previously developed
formalism of the quark compound bags (QCB).
  Partial-wave analysis of nucleon-nucleon scattering indicates the existence
of 6QS which manifest themselves as poles of $P$-matrix. In the framework of
the QCB model, we formulate a self-consistent system of coupled equations for
the nucleon and 6QS propagators in nuclear matter and the G-matrix. The
approach provides a link between high-density nuclear matter with the MQS
components and the cumulative effect observed in reactions on the nuclei, which
requires the admixture of MQS in the wave functions of nuclei kinematically.
  6QS determine the natural scale of the density for a possible phase
transition into the MQS phase of nuclear matter. Such a phase transition can
lead to dynamic instability of newly born protoneutron stars and dramatically
affect the dynamics of supernovae. Numerical simulations show that the phase
transition may be a good remedy for the triggering supernova explosions in the
spherically symmetric supernova models. A specific signature of the phase
transition is an additional neutrino peak in the neutrino light curve. For a
Galactic core-collapse supernova, such a peak could be resolved by the present
neutrino detectors. The possibility of extracting the parameters of the phase
of transition from observation of the neutrino signal is discussed also.
