Extended Harper's model arises in a quantum description of a 2d- crystal layer subjected to an external magnetic field. As a first step towards the spectral analysis we shall introduce the Lyapunov exponent and present a
method of computation valid for any analytic cocycle with possible singularities. This enables us to give a description of the metal-insulator properties for extended Harper's model, which so far did not even exist on a heuristic level in physics literature. We finish the
talk with some results on the spectral analysis of the model.