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The linear electrooptic effect is reviewed with emphasis on understanding the implications of crystal symmetry with regard to device performance. The index changes and the rotations of the index ellipsoid are calculated in detail for each of the 18 biaxial and uniaxial electrooptic crystal classes, and for an applied field of arbitrary direction. For most crystal classes, the EO effect exhibits orthogonality where the index changes and the ellipsoid rotation are proportional to orthogonal components of the applied field. Explicit expressions are given in each crystal class for the electrooptic parameters of selected attractive EO device configurations.