This talk will give a graduate level introduction to the inverse boundary value problem of Calderon, its applications to medical and geophysical imaging, and its analysis using exponentially growing solutions of an elliptic equation. Several open problems in the field will also be presented. In the anisotropic case, the problem becomes one of recovering a metric in a Riemannian manifold with boundary from the corresponding Dirichlet-to-Neumann map for the Laplace-Beltrami operator. This leads to beautiful connections to differential geometry which will be further brought out in several of the lectures in the Symposium.