Oliver F. Piattella, Núcleo Cosmo-UFES and PPGCosmo, Physics Department, Federal University of Espírito Santo, Vitória, ES, Brazil.

Provides an in-depth introduction to cosmology for beginners including open problems and very recent topics such as the synchronicity problem

Functional appendices contain the necessary physics background as a reminder to students making the book self-contained

Exercises in the text complete the derivations of the results, whose ideas and logical steps are carefully outlined

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.