| Introduction | p. 1 |
| Statement of the main results | p. 1 |
| An heuristic justification | p. 22 |
| Discussion of theorem 1.1.6 | p. 24 |
| Higher order wave front sets | p. 33 |
| Higher order wave front sets | p. 34 |
| [actual symbol not reproducible]-microlocalization | p. 44 |
| Splitting and approximation of entire functions | p. 49 |
| Higher microlocalization and duality | p. 55 |
| Plurisubharmonic functions related to propagation phenomena | p. 57 |
| An improvement of proposition 2.5.10 | p. 66 |
| Proof of theorem 2.1.12 | p. 70 |
| Proof of theorem 2.1.13 | p. 73 |
| Proof of proposition 2.1.15 | p. 74 |
| A.1 Propagation of analyticity for partially holomorphic functions | p. 79 |
| A.2 Proof of lemma 2.5.1 | p. 83 |
| A.3 Proof of proposition 2.1.7 | p. 86 |
| Pseudodifferential operators | p. 95 |
| Polyhomogeneous structures and polycones | p. 96 |
| Polyhomogeneity and polyhomogeneous symbols | p. 102 |
| Symbol classes and pseudodifferential operators in general [actual symbol not reproducible]-microlocalization | p. 107 |
| Pseudodifferential operators in k-microlocalization | p. 110 |
| Polyhomogeneity and symbols | p. 116 |
| Finite sums of polyhomogeneous functions and principal parts. Relative Poisson brackets | p. 118 |
| Successive localizations | p. 123 |
| Regularity theorems I | p. 125 |
| Regularity theorems II. Proof of theorem 1.1.6 | p. 127 |
| Improvements in the case of constant coefficient operators | p. 129 |
| Proof of proposition 3.10.3 | p. 134 |
| Proof of the propositions 1.1.9 and 1.1.12 | p. 137 |
| Remarks on localization of polynomials. Proof of proposition 1.1.13 | p. 141 |
| Bi-symplectic geometry and multihomogeneous maps | p. 145 |
| Polyhomogeneous changes of coordinates in R[superscript n] | p. 146 |
| Polyhomogeneous changes of coordinates in R[superscript 2n] | p. 150 |
| Bihomogeneous approximations of homogeneous maps | p. 153 |
| The bihomogeneous structure of N[Sigma] | p. 157 |
| The canonical foliation and the relative tangent space of N[Sigma] | p. 161 |
| The bisymplectic structure of N[Sigma] | p. 163 |
| The relative bicharacteristics foliation of [Lambda] | p. 168 |
| Phase functions and bihomogeneous approximations of canonical maps | p. 170 |
| Construction of the phase | p. 181 |
| Reduction of p[subscript m] to model form, inequalities and a regularity theorem | p. 186 |
| Canonical transformations and estimates for symbols | p. 190 |
| Fourier Integral Operators | p. 193 |
| Classical F.I.O.'s which leave [actual symbol not reproducible]= 0 invariant | p. 194 |
| Invariant definition of [actual symbol not reproducible] | p. 204 |
| F.I.O. associated with phase functions which live on bineighborhoods | p. 206 |
| Phase functions associated with Lipschitzian weight functions | p. 212 |
| Composition of F.I.O. | p. 215 |
| Invariant meaning and proof of theorem 1.1.3 | p. 222 |
| Conical refraction, hyperbolicity and slowness surfaces | p. 225 |
| Influence domains and bicharacteristics | p. 226 |
| The canonical form of operators when [actual symbol not reproducible] is second order and hyperbolic | p. 232 |
| The case when p[subscript m,k] is hyperbolic | p. 235 |
| Singular points on surfaces | p. 254 |
| Remarks on the velocity, the slowness and the wave surface | p. 262 |
| Singular points on the slowness surface and conical refraction | p. 266 |
| Conical refraction in free space for the system of crystal optics | p. 270 |
| Singular points on the slowness surface of the system of elasticity for cubic crystals | p. 273 |
| Propagation of regularity up to the boundary | p. 279 |
| Interior regularity when the traces are smooth | p. 280 |
| Extension across hypersurfaces of solutions of constant coefficient microlocally hyperbolic operators | p. 281 |
| The wave front set of a restriction | p. 286 |
| Estimates for the Fourier transform of some surface densities | p. 289 |
| Boundary values and partial regularity | p. 293 |
| Regularity up to the boundary | p. 299 |
| Proof of lemma 7.6.5 | p. 305 |
| Extension of solutions from the interior | p. 307 |
| Some results on transmission problems | p. 309 |
| Formulation of the problem | p. 310 |
| Regularity of traces as a consequence of interior regularity, I | p. 312 |
| Regularity of traces as a consequence of interior regularity, II | p. 321 |
| Incoming and outgoing bicharacteristics and propagation cones | p. 322 |
| Conical refraction in transmission problems | p. 329 |
| Conical reflection at the boundary | p. 333 |
| The case of crystal optics | p. 335 |
| Other phenomena: External conical refraction | p. 342 |
| Partial analyticity, higher microlocalization and sheaves | p. 347 |
| The [actual symbol not reproducible]-class of a partially analytic distribution | p. 348 |
| The first two wave front sets and partial analyticity | p. 350 |
| Proof of proposition 9.1.2 | p. 351 |
| Review of hyperfunctions | p. 353 |
| Hyperfunctions and real analytic functionals | p. 358 |
| Partially analytic distributions and infinite order operators | p. 361 |
| Proof of proposition 9.1.3 | p. 362 |
| The sheaf of partially analytic microfunctions | p. 366 |
| Second microlocalization and sheaves | p. 368 |
| The Fourier transform of measures on C[superscript n] with supports concentrated on polycones | p. 371 |
| Higher order wave front sets and boundary values of holomorphic functions | p. 374 |
| References | p. 380 |
| Notations | p. 385 |
| Subject index | p. 387 |
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