A detailed study of the aberrations of anamorphic optical systems is presented. This study has been developed with a theoretical structure similar to that of rotationally symmetric optical systems (RSOS) and can be considered a generalization.A general method of deriving the monochromatic primary aberration coefficient expressions for any anamorphic system types with double plane symmetry has been provided.The complete monochromatic primary aberration coefficient expressions for cylindrical anamorphic systems, toroidal anamorphic systems and general anamorphic systems with aspheric departure have been presented, in a form similar to the Seidel aberrations of RSOS.Some anamorphic image system design examples are provided that illustrate the use and value of the theory developed.