Approved for public release, distribution is unlimited / Radar polarimetry is a recent development seeing active research only in the last few decades. The phenomenon that optimal (maximal power) reflected fields exist in both the co-polarized and cross polarized channels of the receiving radar antenna was first introduced by Kennaugh and Huynen. Current research efforts focus on target scattering matrices and relating them to physical attributes of the target. This thesis provides a comprehensive survey of the polarimetry theories that have been put forth by various researchers to characterize, manipulate and optimize target radar returns via polarization states. One such theory is the Target Decomposition (TD) theorem that seeks to decompose the target returns into individual scattering mechanisms. The topic of optimization of polarization states of the incident field for maximizing power return is also examined. Two models are implemented in Matlab to verify and demonstrate these polarimetry theories. The first model uses TD theorems to simulate foliage clutter and study its effect on the polarization of the incident electric field. A (simulated) static dihedral target is introduced and its effect on wave polarization is also simulated. The second model studies optimization of polarization states. Both models are able to produce the expected results for known canonical targets. / Civilian, Republic of Singapore