11-15E

This article is a continuation of previous works [16--23], where we have described the behavior of a simple system of interacting particles in the region of temperatures at and about the critical point, $T\geq T_c.$ A description of the behavior of the system is given at the critical point $(T_c, \eta_c)$ and in the region below the critical point. The calculation is carried out from the first principles. The expression for the grand canonical partition function is brought to the functional integrals defined on the set of collective variables. The Ising-like form is singled out. The equation of state is derived. Below $T_c$, when a gas-liquid system undergoes a phase transition of the first order, i.e., boiling, a ``jump'' occurs from the ``extreme'' high probability gas state to the ``extreme'' high probability liquid state, releasing or absorbing the latent heat of the transition. The phase equilibria conditions are also derived.