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A comprehensive description of the Hansen theory of satellite orbit calculation, as modified by Musen, is presented. The equations of the theory are developed in sufficient detail to allow the reader to relate them to fundamental laws of celestial mechanics. The physical and mathematical concepts underlying Hansen's coordinate system and auxiliary ellipse are treated. The disturbing potential function and its derivatives are developed in the derivation of equations for the perturbations in the orbit plane, as well as the perturbations of the orbit plane. The method is described for determination of the final position and velocity vectors of the real satellite and determination of the osculating elements. Finally, a brief evaluation of the theory is presented.