Gel'fand inverse boundary problem consists of determination of an unknown elliptic operator on a bounded domain/manifold from the restriction to the boundary of its resolvent kernel. This kernel is assumed to be known, as a meromorphic operator-valued function, for all values of the spectral parameter. In our lectures we concentrate on the case of a Laplace operator on an unknown Riemannian manifold. Using the geometric version of the Boundary Control method we show that the Gel'fand inverse boundary problem is uniquely solvable and provide a procedure to recover the manifold and the metric. Using the theory of geometric convergence, we also study geometric conditions on an unknown manifold to guarantee stability of this inverse problem.