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We review the calculations of the kinetic coefficients (thermal conductivity, shear viscosity, momentum transfer rates) of the neutron star core matter within the framework of the Landau Fermi-liquid theory. We restrict ourselves to the case of normal (i.e. non-superfluid) matter. As an example we consider simplest $npeμ$ composition of neutron star core matter. Utilizing the CompOSE database of dense matter equations of state and several microscopic interactions we analyze the uncertainties in calculations of the kinetic coefficients that result from the insufficient knowledge of the properties of the dense nuclear matter and suggest possible approximate treatment. In our study we also take into account non-quantizing magnetic field. The presence of magnetic field makes transport anisotropic leading to the tensor structure of kinetic coefficients. We find that the moderate ($B\lesssim 10^{12}$ G) magnetic field do not affect considerably thermal conductivity of neutron star core matter, since the latter is mainly governed by the electrically neutral neutrons. In contrast, shear viscosity is affected even by the moderate $B\sim 10^8 - 10^{10}$ G. Based on the in-vacuum nucleon interactions we provide practical expressions for calculation of transport coefficients for any equation of state of dense matter.