This book aims at giving the basis of primordial cosmology. The book is self-contained in the sense that all the elements for the derivations of the presented results are given. It can be used as a textbook to study cosmology. It is divided into 3 parts. Part 1 summarizes the fundamentals in theoretical physics needed in cosmology (general relativity, field theory, particle physics). Part 2 describes the standard model of cosmology and includes cosmological solutions of Einstein equations, hot big bang model, cosmological perturbation theory, cosmic microwave background anisotropies, lensing and evidences for dark matter, and inflation. Part 3 describes extensions of this model and opens up to today's research in the field: scalar-tensor theories, supersymetry, the cosmological constant problem and acceleration of the universe, topology of the universe, grand unification and baryogenesis, topological defects and phase transitions, string inspired cosmology including branes and latest developments. The book provides details of all derivations and leads the student up to the level of research articles.