### 1. Introduction.

History of the problem. Einstein relation. Diffusion and “memory”. Experimental evidences of the localization.

### 2. Anderson Model.

Models of Disorder. Anderson model. Von Neumann & Wigner “no crossing rule”. Resonances and qualitative physical picture. Localization in high dimensions–Anderson’s arguments.

### 3. Localization at low dimensions. Scaling theory.

History of the localization in one and two dimensions. Thouless energy and dimensionless Thouless conductance. Intuitive scaling picture. β–function and its asymptotic behavior.

### 4. Weak Localization.

Physics of the 2D localization. Quantum corrections to the conductivity. AC conductivity. Dephasing rate. Temperature dependence of the conductivity.

### 5. Anomalous Magnetoresistance.

History of the problem. Localization in the presence of magnetic field. Aharonov–Bohm effect.

### 6. Theory of the dephasing.

Sources of the dephasing. Magnetic impurities. Inelastic collisions.

### 7. Mesoscopic (sample to sample) fluctuations.

### 8. Interaction between the electrons in the weak localization regime.

### 9. Spectral Statistics and Localization.

Random Matrix theory. “Repulsion” of the energy levels. Wigner-Dyson and Poisson statistics. Dyson ensembles. Spectral statistics as signatures of the localization.

### 10. Localization beyond the real space.

Examples. Localization and quantum chaos. Quantum localization and KAM–theorem for the classical dynamical systems.

### 11. Many-Body Localization.

General remarks and examples. Generalized Ising model and localization on the hypercube. Irreversibility.

### 12. Many-Body Localization of the interacting fermions.

Extended Anderson model. Idea of the calculation. Hoping conductivity and cascades.
Ergodic and non-ergodic metals.

### 13. Many-Body localization of weakly interacting bosons.

Superfluid-Glass transition in the presence of disorder. Normal fluid at finite temperatures.