  This review is devoted to the Multiple Point Principle (MPP), according to
which several vacuum states with the same energy density exist in Nature. The
MPP is implemented to the Standard Model (SM), Family replicated gauge group
model (FRGGM) and phase transitions in gauge theories with/without monopoles.
Lattice gauge theories are reviewed. The lattice results for critical coupling
constants are compared with those of the Higgs Monopole Model (HMM), in which
the lattice artifact monopoles are replaced by the point-like Higgs scalar
particles with a magnetic charge. Considering our (3+1)-dimensional space-time
as discrete, for example, as a lattice with a parameter a=\lambda_P, equal to
the Planck length, we have investigated the additional contributions of
monopoles to beta-functions of renormalization group equations in the FRGGM
extended beyond the SM at high (the Planck scale) energies. We have reviewed
that, in contrast to the Anti-grand unified theory (AGUT), there exists a
possibility of unification of all gauge interactions (including gravity) near
the Planck scale due to monopoles. The unifications [SU(5)]^3 and [SO(10)]^3 at
the GUT-scale \sim 10^{18} GeV are briefly discussed.

High Energy Physics - Phenomenology;High Energy Physics - Lattice;High Energy Physics - Theory