This volume contains a slected number of articles based on lectures delivered at the IMA 2001 Summer Program on Geometric Methods in Inverse Problems and PDE Control. This program was focused on a set of common tools that are used in the study of inverse coefficient problems and control problems for partial differential equations, and in particular on their strong relation to fundamental problems of differential geometry. Examples of such tools are Dirichlet-to-Neumann data boundary maps, unique continuation results, Carleman estimates, microlocal analysis and the so-called boundary control method. Examples of intimately connected fundamental problems in differential geometry are the boundary rigidity problem and the isospectral problem. The present volume provides a broad survey of recent progress concerning inverse and control problems for PDEs and related differential geometric problems. It is hoped that it will also serve as an excellent ``point of departure" for researchers who will want to pursue studies at the intersection of these mathematically exciting, and practically important subjects.

On the construction of isospectral manifolds.- Statistical stability and time-reversal imaging in random media.- A review of selected works on crack identification.- Rigidity theorems in Riemannian geometry.- The case for differential geometry in the control of single and coupled PDEs: the structural acoustic chamber.- Energy measurements and equivalence of boundary data for inverse problems on non-compact manifolds.- Ray transform and some rigidity problems for Riemannian metrics.- Unique continuation problems for partial differential equations.- Remarks on Fourier integral operators.- The Cauchy data and the scattering relation.- Inverse resonance problem for Z2-symmetric analytic obstacles in the plane.- List of workshop participants.