Bogolyubov's inequalities in systems of many interacting particles with broken symmetry

On the basis of the concept of quasiaverages and Bogolyubov's inequalities for the commutator Green's functions, we discuss some problems in many-particle systems in which spontaneous symmetry breaking is manifested physically in quite different ways: the Ising model, the Heisenberg model with ferro-, antiferro-, and ferrimagnetic ordering, systems of superfluid and superconducting type, and a system with crystalline ordering.