A generic phenomenological theory of the glass transition is developed in the framework of a quasilinear formulation of the thermodynamics of irreversible processes. Starting from one of the basic principles of this science in its approximate form given by de Donder's equation, after a change of variables the temperature dependence of the structural parameter xi(T), the thermodynamic potentials Delta (G) over tilde(T), the thermodynamic functions and the time of molecular relaxation tau of vitrifying systems is constructed. In doing so, a new effect in the Delta (G) over tilde(T) course is observed. The analysis of the higher derivatives of the thermodynamic potential, and especially the nullification of the second derivative of the configurational specific heats Delta (C) over tilde(p)(T) of the vitrifying liquid defines glass transition temperature (T) over tilde(g) and leads directly to the basic dependence of glass transition kinetics: the Frenkel-Kobeko-Reiner equation. The conditions guaranteeing the fulfillment of this equation specify the temperature dependence of the activation energy U(T,<(xi)over tilde>) for viscous flow and give a natural differentiation of glass formers into fragile and strong liquids. The effect of thermal prehistory on the temperature dependence of both thermodynamic functions and kinetic coefficients is established by an appropriate separation of de Donder's equation.