The theory of correctness of problems for the Smoluchovsky equation modeling the processes of coagulation (fusion) of particles in dispersed systems. is presented. Spatially homogeneous and non-homogeneous problems. The theorems of global solvability and correctness of the Cauchy problem have been proved. The effects of the transition of the conservation ratio to the dissipation ratio are described and their relationship with the occurrence of non-smooth features of solutions. is revealed. Approximate methods of problem solving are proposed and their justification is given. In classes of functional solutions the approach to allocation of conditions of correctness of problems for equations of Boltzmann type including classical equations of Boltzmann's kinetic theory of gases and Smoluchovsky's kinetic theory of coagulation is described. For researchers, faculty, graduate students and students engaged in mathematical model research in physical kinetics, colloidal chemistry, biology.