In the first part of this Lecture, we analyze electron motion and effective massMasseffective mass of electron in magnetic fieldFieldmagnetic field. We consider also quantum statisticsQuantum statisticsStatisticsquantum statistics of electrons in metal and electron density of statesDensity of stateselectron density of states. We discuss the band fillingFilling of metals in uncorrelated case. We introduce the double-well potentialPotentialdouble-well potential for the description of the metal–insulator transitionMetal-insulator transitionTransitionmetal-insulator transition in strongly correlated Mott–Hubard regime. We find specific heat of electron gasGaselectron gas in metal and compare electron and phonon contributionsContributionphonon contribution. In the end of the Lecture, we describe Lifshitz topological phase transition.