In the past couple of decades, gravitational lensing has gone from being a theoretical possibility to an observational test of general relativity to a method for determining cosmological parameters. Being the only direct and independent way to measure the mass of cosmological objects, it is by far the most promising method of pinning down the value of the density parameter, [Omega]_o, and directly measuring the mass-to-light ratio of the universe at both small and large scales.

As promising as it is, gravitational lensing is hampered by the lack of knowledge of the intrinsic morphology of the sources being lensed. In the strong lensing regime, one is aided by the fact that the distant source is multiply imaged. Each image is a different, highly distorted view of the same source and therefore must reproduce the same morphology when the lens is theoretically removed and therefore gives us the extra constraints needed to gain this knowledge. However, strong lensing is much less likely, and probes smaller length scales, than weak lensing. One therefore needs another way to determine the intrinsic morphology of the source. One way is to use the polarization of the source.

Like wavelength, polarization is an intrinsic property of the photon, which is not altered by gravitational potentials. The path of the photon will be deflected and the image of a source formed by an ensemble of photons will be distorted due to differential bending, yet the polarization of the source remains intact. Polarization therefore gives us a window into the source plane which we can use to constrain the amount of weak and strong gravitational lensing.

This thesis will examine the effects of gravitational lensing on polarized sources in the strong and weak lensing regimes. The theory of the gravitational lens and its role in cosmology will be presented as well as general considerations of cosmological observations in a non-homogeneous universe. Next, the theoretical predictions of the effects of gravitational lensing, both strong and weak, on polarized sources will be presented. Finally, this theoretical framework will be applied to several astronomical objects which produce polarized radiation.