This paper examines the polarization aberrations in optical systems of isotropic radially symmetric weak polarizers in the paraxial approximation. Optical systems which fit this description are composed of uncoated and coated lenses and mirrors. Polarization aberrations are variations in phase, amplitude, and polarization state of the electromagnetic field across the exit pupil. Some are dependent on the incident polarization state and some are not. Expressions through fourth order for phase, amplitude, linear polarization, and linear retardance aberrations are derived in terms of the chief and marginal ray angles of incidence and Taylor series expansion coefficients of the Fresnel equations for reflection and transmission at interfaces.