A theory of neutron transport which includes polarization effects is developed. We have in mind, in particular, the polarization of fast neutrons that results when they are scattered by unpolarized nuclei—an effect explained by a neutron-nucleus spin-orbit interaction. The polarization of neutrons is described by a quantum-mechanical polarization vector. We first examine the change of this vector in scattering and thence formulate a general transport theory in terms of two coupled transport (Boltzmann) equations for the scalar neutron flux and the vector polarization flux. For plane or spherical geometry we show that the polarization vector is always normal to the (r̂, Ω) plane and thus obtain two coupled scalar transport equations for the flux and this one component of the polarization flux. A spherical harmonics solution is developed wherein the neutron flux is expanded in Legendre polynomials and the polarization flux is expanded in associated Legendre functions of the first kind. In the P1 approximation the effect of polarization on the neutron flux is obtained by simply increaSing the transport cross section. The polarization flux is then proportional to the neutron current (as a function of position) times sin θ with cos θ = r̂·Ω, as usual. Higher-order spherical-harmonics values are found for the asymptotiC diffusion length, and numerical results are calculated for neutrons scattered from uranium. We conclude that the P1 theory can be used to obtain a reasonable estimate of the polarization effects and that the changes in diffusion length due to polarization are generally small, but may be a few percent for the energy range where the p wave scattering is important. The polarization of neutrons in a multiplying assembly should be experimentally observable.