Reconstruction of the conductivity of a medium from a set of known values of the boundary potential and boundary normal current is described. The geometry is general, two or three dimensional. The method is applied to two cases, a circular medium and an infinite medium under a plane. In both cases the conductivity is found as an expansion on a system of orthogonal functions. In a linear approximation the conductivity may explicitly be reconstructed. The problem is an ill posed one, the condition numbers are found. Some numerical examples are included.