§16§§In inverse problems, the aim is to obtain, via a mathematical model, §04§I. EMS Summer School: New Analytic and Geometric Methods in Inverse Problems.- Metric Geometry.- Intertwining Operators in Inverse Scattering.- Carleman Type Estimates and Their Applications.- Gaussian Beams and Inverse Boundary Spectral Problems.- Analytic Methods for Inverse Scattering Theory.- Ray Transform on Riemannian Manifolds.- On the Local Dirichlet-to-Neumann Map.- II. EMS Conference: Recent Developments in the Wave Field and Diffuse Tomographic Inverse Problems.- Remarks on the Inverse Scattering Problem for Acoustic Waves.- Asymptotic Properties of Solutions to 3-particle Schrödinger Equations.- Stability and Reconstruction in Gel'fand Inverse Boundary Spectral Problem.- Uniqueness in Inverse Obstacle Scattering.- Geometric Methods for Anisotopic Inverse Boundary Value Problems.- Applications of the Oscillating-Decaying Solutions to Inverse Problems.- Time-Dependent Methods in Inverse Scattering Theory.