I. Scattering by an Obstacle.- 1. Statement of the Problem. Basic Integral Equations.- 2. Existence and Uniqueness of the Solution to the Scattering Problem.- 3.

Eigenfunction Expansion Theorem.- 4. Properties of the Scattering Amplitude.- 5. The S-Matrix and Wave Operators.- 6. Inequalities for Solutions to Helmholtz's Equation for Large frequencies.- 7.

Representations of solutions to Helmholtz's Equation.- II. The Inverse Scattering (Diffraction) Problem.- 1. Statement of the Problem and Uniqueness Theorems.- 2. Reconstruction of Obstacles from the Scattering Data at High Frequencies.- 3.

Stability of the Surface with Respect to Small Perturbations of the Data.- III. Time Dependent Problem.- 1. Statement of the Problems.- 2. The Limiting Amplitude Principle (Abstract Results).- 3.

The Limiting Amplitude Principle for the Laplacian in Exterior Domains.- 4. Decay of Energy.- 5. Singularity and Eigenmode Expansion Methods.- IV. T-Matrix Scheme and Other Numerical Schemes.- 1.

Statement of the Problem.- 2. Justification of the T-Matrix Scheme.- 3. Numerical Results.- 4. Other Schemes.- V.

Scattering by Small Bodies.- 1. Scattering by a Single Small Body.- 2. Scattering by Many Small Bodies.- 3. Electromagnetic Wave Scattering by Small Bodies.- 4.

Behavior of the Solutions to Exterior Boundary Value Problems at Low Frequencies.- VI. Some Inverse Scattering Problems of Geophysics.- 1. Inverse Scattering for Geophysical Problems.- 2. Two Parameter Inversion.- 3.

An Inversion Formula in Scattering Theory.- 4. A Model Inverse Problem of Induction Logging.- VII. Scattering by Obstacles with Infinite Boundaries.- 1. Statement of the Problem.- 2.

Spectral Properties of the Laplacians.- 3. Spectral Properties of the Dirichlet Laplacian in Semi-Infinite Tubes.- 4. Absence of Positive Eigenvalues for the Dirichlet Laplacian Under Local Assumptions at Infinity.- 5. The Limiting Absorption Principle and Compact Perturbations of the Boundary.- 6.

Eigenfunction Expansions in Canonical Domains.- Appendix 1. Summary of some Results in Potential Theory and Embedding Theorems.- Appendix 2. Summary of some Results in Operator Theory.- Appendix 4. Stable Numerical Differentiation.- Appendix 5.

Limit of the Spectra of the Interior Neumann Problems when a Solid Domain Shrinks to a Plane One.- Appendix 6. Construction of a Surface from its Principal Curvatures.- Appendix 7. Resonances.- Research Problems.- Bibliographical Notes.- List of Symbols.