Galvano-magnetic phenomena today and forty years ago

In this review we discuss the basic aspects of the theory of galvanomagnetic phenomena in metals developed by I.M. Lifshitz and his collaborators, assuming a general form for the electron energy spectrum. This theory was the foundation of the spectroscopic method for the examination of the topological structure of the energy spectrum of the charge carriers in metals and in conducting media with a metallic type conductivity (synthetic metals). We analyze the connection of these works made forty years ago with the present state of the studies of electron processes in conductors.