This volume contains the Proceedings of a meeting held at Montpellier from November 27th to December 1st 1989 and entitled "Inverse Problems Multicen­ tennials Meeting". It was held in honor of two major centennials: the foundation of Montpellier University in 1289 and the French Revolution of 1789. The meet­ ing was one of a series of annual meetings on interdisciplinary aspects of inverse problems organized in Montpellier since 1972 and known as "RCP 264". The meeting was sponsored by the Centre National de la Recherche Scientifique (con­ tract GR 264) and by the Direction des Recherches et Etudes Techniques (contract 88 CO 283). The Proceedings are presented by chapters on different topics, the choice of topic often being arbitrary. The chapter titles are "Tomographic Inverse Problems", "Distributed Parameters Inverse Problems", "Spectral Inverse Problems (Exact Methods)", "Theoretical hnaging", "Wave Propagation and Scattering Problems (hnaging and Numerical Methods)", "Miscellaneous Problems", "Inverse Methods and Applications to Nonlinear Problems". In each chapter but the first, the papers have been sorted alphabetically according to author*. In the first chapter, a set of theoretical papers is presented first, then more applied ones. There are so many well-known and excellent lectures that I will not try to refer to them all here (the reader will be easily convinced by reading the Table of Contents). My comments at the conference are summarized by the short scientific introduction at the beginning of the volume.

Table of Contents:
Modelling or Solving Inverse Problems?.- I Tomographic Inverse Problems.- Tomography with Diffusion,.- Medical Imaging: State-of-the-Art and Future Development.- Inverse Problems for Discrete Evolution Models.- Recent Developments in Electrical Impedance Tomography.- Two Inverse Problems for the Exponential Radon Transform.- Tomographic Image Reconstruction from a Limited Set of Projections Using a Natural Pixel Decomposition.- Application of the Simulated Annealing Technique to Microwave Tomography: Preliminary Results.- Elastic Wave Diffraction Tomography.- II Distributed Parameters Inverse Problems.- Non-linear Least-Square Theory for Inverse Problems.- Circulant Preconditioners for Non-negatively Constrained Deconvolution Problems.- Tikhonov Regularization of Nonlinear Differential-Algebraic Equations.- On the Choice of the Regularization Parameter Using Model Functions.- Exact Reconstruction Procedures for Some Multidimensional Inverse Scattering and Inverse Boundary Value Problems.- On the Discretization and Regularization of Selfadjoint Ill-Posed Problems.- Age Structured Population Dynamics.- Ball Stabilization in Inverse Problems.- III Spectral Inverse Problems.- Algorithms for Solving Inverse Eigenvalue Problems for Sturm-Liouville Equations.- Inverse Problem in the Coupling Constant.- Examples of Inverse Nodal Problems.- Conditions on the Data in Inverse Problems in Vibration.- An Inverse Eigenvalue Problem and an Extremal Eigenvalue Problem.- IV Scattering Inverse Problems (Exact Methods).- Scattering by Black-Hole for Electromagnetic Fields.- Phase Space and Functional Integral Methods in Direct and Inverse Scattering.- New Results on 3D Schrödinger Inverse Scattering.- Electromagnetic Inverse Problems at Low Frequencies.- Retrieval of a Time-DependentSource in an Acoustic Propagation Problem.- Inverse Scattering Problems for the Wave Equation with Time Dependent Impurities.- Wave Splitting and the Reflection Operator for the Wave Equation.- Multidimensional Inverse Quantum Scattering Problem and Wiener-Hopf Factorization.- The Direct and Inverse Scattering Transforms for a Sturm-Liouville Equation on Finite Interval as Smooth Maps. The Geometry of a Set of Finitely-Zoned Potentials.- V Theoretical Imaging.- Application of Singular Systems to Some Data Reduction Problems in Modern Optics.- Temporal Homogenization.- Reciprocity, Discretization, and the Numerical Solution of Direct and Inverse Acoustic Radiation and Scattering Problems.- A Quadratic Inverse Problem: The Phase Retrieval.- VI Wave Propagation and Scattering Problems (Imaging and Numerical Methods).- Numerical Investigation of the Probing of Sea-Bottoms Using Exact and Approximate Methods.- Quantitative Reconstruction of Complex Permittivity Distributions by Means of Microwave Tomography.- Some Asymptotic Results on Coherent-State Matrix Elements.- Inverse Problems for Dispersive Biological Media.- Image Estimation from Scattered Field Data (at 10 GHz) Using the Distorted Wave Born Approximation and Other Prior Knowledge.- Phase Equivalence Between Nonlocal and Local Potentials Using Inversion and Supersymmetry.- Inverse Scattering Theory for Phase-Conjugate Reflection Coefficients: Application to Optical Switching.- An Inverse Problem in Propellant Combustion.- Inversion of Three-Quark Spectral Data.- Stability and Convergence in the ID Time-Dependent Problem.- Inverse Profiling for an Inhomogeneous, Plane-Stratified Lossy Causal Medium.- VII Miscellaneous Problems.- Some Remarks on the Relationship Between Mathematics and Physics and on Inverse Problems.- Variational Averaging of Problems with Stochastic Data.- Some High Energy Cross Sections from an Inverse Point of View.- Exact Shock Wave Solutions for an 8v? Discrete Boltzmann Model with Temperature.- Teaching Direct and Inverse Problems by Means of User Friendly Interfaces: A Status Report.- Quantum Inverse Scattering Theory and Nucleon-Nucleon Potentials.- Generalized Backus-Gilbert Methods.- Inversion of Ionospheric Sounding Data from an HF Backscatter Radar.- Generalized Bargmann-Type Potentials.- Rigorous Computer Solutions of Infinite-Dimensional Inverse Problems.- Seismic Waveform Inversion Using a Layer-Stripping Method.- Highly Dimensional, Highly Non-linear Inverse Problems in Geophysics.- Numerical Construction of Nonlinear Wave Train Solutions of the Periodic Korteweg-de Vries Equation.- VIII Inverse Methods and Applications to Nonlinear Problems.- The Meld Factorization in Relation to Various Problems in Mathematical Physics.- Some Ideas on Nonlinear Evolution Equations.- Painlevé Singular Manifold Equation and Integrability.- The Davey-Stewartson 1 Equation: A Class of Explicit Solutions Including the Special Case of the Dromions.- The “IST” as a Diagnostic Tool for Perturbed Nonlinear Schrödinger Systems.- Gaps of One-Dimensional Periodic AKNS Systems.- Combinatorial Aspects of Some Classes of Linearizable and Bilinearizable NLPDEs.- An Integrable Model for Small Amplitude Nonlinear Coupled Waves Produced During Laser-Plasma Interaction.- On the Spectral Theory of the Davey-Stewartson Equation.- Multidimensional Solitons in Terms of Fermions.- On the AMCP Functional Equation for the Solvable Chiral Potts Model.- Painlevé-Darboux Transformation in Nonlinear PDEs.- Solitons and Spectral Transform for the Kadomtsev-Petviashvili Equation.-Dromions, a New Manifestation in Nonlinear Phenomena.- The Phoenix Equation.- On the Dressing Method.- Index of Contributors.- Conference Program.