Preface -- Notation -- Cosmology -- The expanding universe and its content -- Cosmological observations -- Redshift -- Open problems in cosmology -- The universe in expansion -- Newtonian cosmology -- Relativistic cosmology -- Friedmann equations -- Solutions of the Friedmann equations -- Distances in cosmology -- Thermal history -- Thermal equilibrium and Boltzmann equation -- Short summary of thermal history -- The distribution function -- The entropy density -- Photons -- Neutrinos -- Boltzmann equation -- Boltzmann equation with a collisional term -- Big-Bang Nucleosynthesis -- Recombination and decoupling -- Cosmological perturbations -- From the perturbations of the FLRW metric to the linearised Einstein tensor -- Perturbation of the energy-momentum tensor -- The problem of the gauge and gauge transformations -- Normal mode decomposition -- Einstein equations for scalar perturbations -- Einstein equations for tensor perturbations -- Einstein equations for vector perturbations -- Perturbed Boltzmann equations -- General form of the perturbed Boltzmann equation -- Force term -- The perturbed Boltzmann equation for CDM -- The perturbed Boltzmann equation for massless neutrinos -- The perturbed Boltzmann equation for photons -- Boltzmann equation for baryons -- Initial conditions -- Initial conditions -- Evolution equations in the kn^Inflation -- The flatness problem -- The horizon problem -- Single scalar field slow-roll inflation -- Production of gravitational waves during inflation -- Production of scalar perturbations during inflation -- Spectral indices -- Observational results -- Examples of models of inflation -- Evolution of perturbations -- Evolution on super-horizon scales -- The matter-dominated epoch -- The radiation-dominated epoch -- Deep inside the horizon -- Matching and CDM transfer function -- The transfer function for tensor perturbations -- Anisotropies in the Cosmic Microwave Background -- Free-streaming -- Anisotropies on large scales -- Tight-coupling and acoustic oscillations -- Diffusion damping -- Line-of-sight integration -- Finite thickness effect and reionization -- Cosmological parameters determination -- Tensor contribution to the CMB TT correlation -- Polarisation -- Miscellanea -- Bayesian analysis using type Ia supernovae data -- Doing statistics in the sky -- Appendices -- Thermal distributions -- Derivation of the Poisson distribution -- Helmholtz theorem -- Conservation of R on large scales and for adiabatic perturbations -- Spherical harmonics -- Method of Green's functions -- Polarisation -- Thomson scattering -- Bibliography -- Subject Index.