The resistivity of metals with non-magnetic impurities is calculated using the microscopic Fermi liquid theory based on the Keldysh temperature technique. Such low temperatures are considered that the quasiclassical description of the kinetic processes is inapplicable, i.e. T<c thetaD for the electron-phonon interaction and T<cEF for the Coulomb electron-electron interaction (where c denotes the concentration of the defects). The temperature dependence of the resistivity in the temperature region considered arises from the electron-electron interaction interfering with the impurity scattering. Such interference results in the diffusion amplification of the two-particle interaction amplitudes. The electron-phonon interaction gives a negligibly small contribution to the resistivity when T<c theta , as compared with that of the Coulomb interaction, since the scattering by 'pure' phonons is largely compensated by that of the vibrating impurities. The Coulomb interaction between the electrons which are scattered by static impurities results in decreasing resistivity versus increasing temperature according to Delta rho (T) approximately -c5/2(T/EF) 1/2; for T>or approximately=c thetaD(theta D/EF)1/3 this law is replaced by the dependence Delta rho (T) approximately c(T/ theta D)2, i.e. the curve Delta rho (T) possesses a minimum.