Abstract: In order to investigate the polarization state variation of the light passing through transparent optical crystals and to evaluate the optical characteristics of crystals with polarizing microscope, the optical structure of the polarizing microscope was introduced, the geometrical optical path which natural light went through in the polarizing microscope was analyzed, and the polarization state transformation happened when the natural light passed through the polarizing microscope was investigated with Stokes parameters and Muller matrix. The principle of polarization state transformation was given theoretically. The theoretical fundamentals are provided for operating the polarizing microscope and understanding its operation principle.