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The basic concepts of the theory of Anderson localization are reviewed in the example of electrons in disordered solids. The lectures are organized in three sections. In the first, the phenomenon of localization of quantum particles or classical waves is introduced on a qualitative level. The regimes of strong and weak localization are discussed. Sample to sample fluctuations are considered for one-dimensional and quasi–one-dimensional systems. In sect. 2 the scaling theory of the Anderson localization transition is presented. The renormalization group theory is introduced and results and consequences are presented. The classification of the Anderson transitions into universality classes is described. Basic concepts of the fractal structure of the wave functions at the critical point are reviewed. In sect. 3 the self-consistent theory of Anderson localization is presented. The effect of the electron-electron interaction in destroying the phase coherence is briefly discussed.
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