In this chapter, we present an inverse problem for the Laplace equation. The direct problem is the Dirichlet problem, where we seek the solution to the Laplace equation in a domain with specified boundary values. The inverse problem arises when a portion of the boundary, called the “inaccessible” part, is unknown, and we are given the normal derivative of the solution on “accessible” part of the boundary. The goal is to determine the inaccessible part based on the given information. This problem is overdetermined, but we can reformulate it as finding a solution to a related equation involving the inaccessible part. The inverse problem then becomes the task of determining the inaccessible part such that a certain condition holds on the boundary, and, in particular on an accessible part.