This paper investigates the metal-insulator transition in a weakly interacting many-electron system with localized single-particle states. The authors show that in the absence of coupling to an external bath, the dc electrical conductivity vanishes at temperatures below a critical value $ T_c $, while at higher temperatures it becomes finite. This implies a finite-temperature metal-insulator transition, which can be viewed as Anderson-like localization of many-body wave functions in Fock space. The metallic and insulating states are not distinguished by any spatial or discrete symmetries. The effective Hamiltonian for the system at low energies is formulated, and the quantum Boltzmann equation is used to determine kinetic coefficients in the metallic phase. In the insulating phase, the probability distribution function for quantum-mechanical transition rates is determined using Feynman diagram techniques. The probability of an escape rate from a given quantum state is found to vanish in every order of perturbation theory in electron-electron interaction, indicating that electron-electron interaction alone cannot cause relaxation or establish thermal equilibrium. When a weak coupling to a bath is introduced, conductivity becomes finite even in the insulating phase. Near the transition temperature, this conductivity is much larger than phonon-induced hopping conductivity of non-interacting electrons. The reason for this enhancement is that the stability of the insulating state decreases as the transition point is approached, allowing a single phonon to cause a cascade of electronic hops. The paper also discusses the microscopic mechanism of the many-body localization transition, showing that the existence of extended many-body states at high energies is an established fact. The authors analyze the correspondence between a many-electron interacting system and the Anderson model on a certain graph, and demonstrate that the many-body localization transition occurs when the system's energy is below a critical value $ E_c $, which is extensive in volume. The transition is shown to be a genuine phase transition, with the system's conductivity becoming finite at $ T = T_c $. The paper concludes that the metal-insulator transition in a weakly interacting many-electron system with localized single-particle states is a result of many-body localization in Fock space, and that the transition is characterized by a critical temperature $ T_c $, which depends on the typical number of electrons within the localization volume and the strength of the electron-electron interaction. The results are supported by a detailed analysis of the system's behavior in both the metallic and insulating phases, and the paper provides a comprehensive framework for understanding the metal-insulator transition in such systems.This paper investigates the metal-insulator transition in a weakly interacting many-electron system with localized single-particle states. The authors show that in the absence of coupling to an external bath, the dc electrical conductivity vanishes at temperatures below a critical value $ T_c $, while at higher temperatures it becomes finite. This implies a finite-temperature metal-insulator transition, which can be viewed as Anderson-like localization of many-body wave functions in Fock space. The metallic and insulating states are not distinguished by any spatial or discrete symmetries. The effective Hamiltonian for the system at low energies is formulated, and the quantum Boltzmann equation is used to determine kinetic coefficients in the metallic phase. In the insulating phase, the probability distribution function for quantum-mechanical transition rates is determined using Feynman diagram techniques. The probability of an escape rate from a given quantum state is found to vanish in every order of perturbation theory in electron-electron interaction, indicating that electron-electron interaction alone cannot cause relaxation or establish thermal equilibrium. When a weak coupling to a bath is introduced, conductivity becomes finite even in the insulating phase. Near the transition temperature, this conductivity is much larger than phonon-induced hopping conductivity of non-interacting electrons. The reason for this enhancement is that the stability of the insulating state decreases as the transition point is approached, allowing a single phonon to cause a cascade of electronic hops. The paper also discusses the microscopic mechanism of the many-body localization transition, showing that the existence of extended many-body states at high energies is an established fact. The authors analyze the correspondence between a many-electron interacting system and the Anderson model on a certain graph, and demonstrate that the many-body localization transition occurs when the system's energy is below a critical value $ E_c $, which is extensive in volume. The transition is shown to be a genuine phase transition, with the system's conductivity becoming finite at $ T = T_c $. The paper concludes that the metal-insulator transition in a weakly interacting many-electron system with localized single-particle states is a result of many-body localization in Fock space, and that the transition is characterized by a critical temperature $ T_c $, which depends on the typical number of electrons within the localization volume and the strength of the electron-electron interaction. The results are supported by a detailed analysis of the system's behavior in both the metallic and insulating phases, and the paper provides a comprehensive framework for understanding the metal-insulator transition in such systems.