Gravitational instabilities in GR and in the Newtonian limit. Jeans wavelength. Diffusion and free- streaming phenomena. Correlation function and power spectrum of density fluctuations. Gaussian statistic and initial conditions. Evolution of the power spectrum in cosmological models. Galaxy correlation function. Dipole anisotropy of the cosmic background and the "great attractor". Intensity and polarization anisotropies of the CMB. Sachs-Wolfe effect. Results from the COBE, WMAP, Planck satellites: the concordance model and the anomalies. Redshift surveys and Baryonic Acoustic Oscillations. Future space missions: Euclid and LiteBIRD satellites.