This set of lectures is devoted to the production, the characterization and the main properties of Bose-Einstein condensates in dilute alkali vapor.

A general introduction on perfect gases will be first proposed. The long quest for the realization of Bose-Einstein condensation in dilute gases will be presented through an historical perspective. The key experimental techniques such as evaporative cooling will be explained and the different possible implementations will be presented.

Atom-atom interactions in the ultracold temperature regime play a crucial role despite the diluteness of the gas. The theoretical description of a condensate at zero temperature will be performed using the Gross-Pitaevskii equation where interactions between particles are taken into account through a mean field term. The analysis of this equation will be done using the hydrodynamic formalism. Such an approach will give the opportunity to work out the main features of Bose-Einstein condensates (BEC): equilibrium profile, Bogolubov spectrum, speed of sound, collective excitation modes, expansion of a BEC after releasing the trap, moment of inertia ...

One of the most intriguing question on degenerate quantum fluids is superfluidity. We will summarize the different experimental efforts along with their theoretical framework to investigate this remarkable property. Bose-Einstein condensates can also be considered as a source of coherent matter waves. This is exemplified by the generation of free falling and guided atom lasers. The different experimental techniques and the properties of atom lasers will be extensively described.