I: Hyperbolic Systems and Equations -- Caractère holonôme d'une solution élémentaire -- Necessary conditions for hyperbolicity of first order systems -- On the Cauchy problem for hyperbolic operators with non-regular coefficients -- Multiple points of the characteristic manifold of a diagonalizable operator -- Large temps de vie des solutions d'un problème de Cauchy non linéaire -- Une remarque sur un prolongement analytique de la solution du problème de Cauchy -- Conormality and lagrangian properties along diffractive rays -- Caractérisation des opérateurs différentiels hyperboliques -- A dependence domain for a class of micro-differential equations with involutive double characteristics -- Ramification non abélienne -- II: Symplectic Mechanics and Geometry -- Extension du calcul différentiel et application à la théorie des groupes de Lie en dimension infinite -- The cohomological meaning of Maslov's lagrangian path intersection index -- A Kähler structure on the punctured cotangent bundle of the Cayley projective plane -- On mechanical systems with a Lie group as configuration space -- Dirac fields on asymptotically simple space-times -- An embedding result for some general symbol classes in the Weyl calculus -- The lagrangian in symplectic mechanics -- Geometry of solution spaces of spaces of Yang-Mills equations -- III: Sheaves and Spectral Sequences -- La theórie des résidus sur un espace analytique complexe -- Derivation of exact triples and Leray-Koszul spectral sequences -- IV: Elliptic Operators; Index Theory -- Le noyau de la chaleur des opérateurs sous-elliptiques des groupes d'Heisenberg -- The geometry of Cauchy data spaces -- On the Cauchy problem for Kirchhoff equations of p-laplacian type -- A remark on surgery in index theory of elliptic operators -- The q invariant and elliptic operators in subspaces -- Regularisation of mixed boundary problems -- V: Mathematical Physics -- Covariant method for solution of Cauchy's problem based on Lie group analysis and Leray's form -- Liouville forms, parallelisms and Cartan connections -- A two-dimensional non-linear shell model of Koiter's type -- A model of the process of thinking based on the dynamics of bundles of branches and sets of bundles of p-adic trees -- Global wave maps on black holes -- Entanglement, parataxy, and cosmology -- Sur le contrôle des équations de Navier-Stokes -- Addresses.