1. Elements of probability theory -- 2. Fluctuations close to thermodynamic equilibrium -- 3. Elements of stochastic processes -- 4. Irreversibility and the Fokker-Planck equation -- 5. Irreversibility and linear response -- 6. Introduction to diffusive transport -- 7. Diffusion in disordered media -- 8. Nonequilibrium statistical mechanics -- 9. Metastable and unstable states -- App. A. Thermodynamic variables in statistical mechanics -- App. B. Relaxation to the stationary state -- App. C. The Green function of the problem of an impurity -- App. D. The waiting-time function of the CTRW -- App. E. Non-Markovian effects against irreversibility -- App. F. The density matrix -- App. G. Kubo's Formula for the susceptibility -- App. H. Fractals -- App. I. Quantum open systems.