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When a fiber is characterized by measured polarization mode dispersion (PMD) vector data, inversion of these data is required to determine the frequency dependence of the fiber's Jones matrix and, thereby, its pulse response. This tutorial reviews the principal concepts and theory employed in approaches to PMD inversion and in the closely related emulation of PMD. We discuss three second-order emulator models and the distinction between the PMD vectors and the eigenvectors of the fiber's Jones matrix. We extend emulation and inversion to fourth-order and sixth-order PMD using higher order concatenation rules, rotations of higher power designating higher rates of acceleration with frequency, and representation of these rotations by Stokes' vectors.