These proceedings reflect the main activities of the Paris S?minaire d'Alg?bre 1989-1990, with a series of papers in Invariant Theory, Representation Theory and Combinatorics. It contains original works from J. Dixmier, F. Dumas, D. Krob, P. Pragacz and B.J. Schmid, as well as a new presentation of Derived Categories by J.E. Bj?rk and as introduction to the deformation theory of Lie equations by J.F. Pommaret. J. Dixmier: Sur les invariants du groupe sym?trique dans certaines repr?sentations II.- B.J. Schmid: Finite groups and invariant theory.- J.E. Bj?rk: Derived categories.- P. Pragacz: Algebro-Geometric applications of Schur S- and Q-polynomials.- F. Dumas: Sous-corps de fractions rationnelles des corps gauches de s?ries de Laurent.- D. Krob: Expressions rationnelles sur un anneau.- J.F. Pommaret: Deformation theory of algebraic and Geometric structures.- M. van den Bergh: Differential operators on semi-invariants for tori and weighted projective spaces.