Various aspects of the transport of neutrons and photons, particularly in slab geometry, have been investigated. One investigation led to the observation that it is possible to write down formal solutions of transport problems in slabs by inspection in terms of the boundary conditions. It was shown previously that solutions of an assortment of problems could be written in terms of a few basic quantities, which occurred again and again. Prescriptions were given to evaluate these quantities. In the present work physical interpretations have been given to each of these quantities. Use of these interpretations obviates the need for any further algebra. A second line of effort extended the Transfer Matrix Method for transport problems to polarized light, e.g., sunlight incident on the atmosphere. The polarization produces a sort of asymmetry--- what appears clockwise looking from one side appears counterclockwise from the other. The generalizations were necessary to apply the method to polarized radiation. A third effont resulted in the determination of the limitations on the Legendre coefficients in order that quadratically anisotropic scattering result in non-negative cross sections. Finally, the eigenvalues of the one-speed transport equation were investigated for two different situations. In one, the medium is multiplying andmore » the scattering is forward-peaked; the eigenvalues can be complex. The other is a neutron wave problem. The behavior of the eigenvalues has been examined as a function of the values of the parameters and families of curves obtained. In these studies the dependence of the solutions obtained on the order of the approximation used was also determined. (auth)« less