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This monograph offers the first comprehensive treatment of the material properties of non-linear electromagnetic elastic crystals through constitutive equations. The lists and tables given in this volume are essential to the discussion of material properties of magnetic crystal classes and for research in the nonlinear electro-magnetic theory of elastic solids. Nonlinear optics, nonlinear magnetism, elastic solids subject to large fields, plasma physics are but a few areas where one needs nonlinear constitutive equations in their final forms. The method and materials provided here should be useful, therefore, to material scientists, engineers, and physicists working in these fields. Several examples of applications to demonstrate the use of the theory are included. The results have been verified by means of computer.