Аннотация:A microscopic theory of weak gels, i.e., systems of identical monomers capable of forming from 0 to f > 2 reversible chemical bonds with other particles at thermodynamic equilibrium, is devised. A new primary approximation is proposed to describe an infinite network of bonds (a gel fraction), and it is used to show that the formation of a gel fraction (a sol-gel transition) in weak gels is a second-order phase transition. At the transition point both the geometric characteristics of the clusters of bonds (which are analogous to the structural characteristics of clusters of conducting bonds in the case of percolation) and the observable physical (thermodynamic) parameters are singular. In view of the fundamental importance of this result, it is obtained in three totally different ways: 1) in terms of formal derivatives of functions from the physically visualizable diagram technique, which makes it possible to analyze the decisive role of the cyclization effects accompanying a sol-gel transition; 2) by generalizing the approach developed by I. M. Lifshits in the theory of polymer globules on the basis of density-functional formalism; 3) by employing an approximation for the statistical sum of the grand canonical ensemble of the system under consideration by a certain two-field functional integral. The abrupt changes in the thermodynamic derivatives are calculated in that approximation, and the features of the density-density correlation function near the sol-gel transition point are found.