The method of covariant field theory at finite temperature is applied to the propagation of neutrinos in a medium. The implications due to the discrete space-time symmetries on the dispersion relations are derived. In the calculation of rates for processes involving neutrinos, the neutrino wave functions that must be used differ from those in a vacuum by some normalization factors that depend on the medium. The calculation of these normalization factors is described and general formulas are obtained in terms of the neutrino self-energy in the medium. As an example of the formalism the Wolfenstein formula for the index of refraction of a neutrino propagating through a gas of electrons is rederived. Also, the dispersion relations and wave functions are calculated for the case of a neutrino background, in the presence of new interactions mediated by a light scalar.