SAP, a symbolic algebraic processor. Andre Deprit U.S. National Institute of Standards and Technology, Gaithersburg, MD 20899--0001, U.S.A. and Grupo de Mecanica Espacial, Universidad de Zaragoza, 50009 Zaragoza, Spain Phone and Fax: 34 76 35 70 11 e-mail: deprit@enh.nist.gov Various algebraic structures like vectors, quaternions, polynomials, algebras of trigonometric functions or vector fields may be represented in MATHEMATICA as programming objects. The context mechanism of MATHEMATICA, however crude, is sufficient to define inheritance among structures. Each package of code is accompanied by an extensive section of checks and illustrations designed to provide rapid signals whenever modifications have been made in the package itself or anywhere in the line of its ascendants. Special effort is made for protecting users against calls to procedures outside the conditions imposed by SAP. On the whole, SAP aims at implementing the perturbation techniques originating from the theory of Lie transformations in non linear dynamics, especially in celestial dynamics and in the semi classical schemes of molecular physics. Its friendliness and flexibility are continuously checked in the most diverse circumstances from refereeing papers to keeping in running condition the calculations substantiating manuscripts prepared for publication. It has made possible, for instance, to revise in depth the literature of the past ten years about drag force in Point Dynamics, to reframe Stiefel's theory of the KS transformation within the theory of quaternions. All the formulas in the Tables of Elliptic Integrals by Byrd and Freedman can now been obtained aumotacially. Work is in progress for the construction of analytical theories for artificial satellites.