Bose-Einstein condensation: a window on the quantum world

The Bose-Einstein condensation (BEC) of dilute atomic gases is one of the most fascinating quantum phenomena. It essentially realizes the macroscopic coherent occupation of only one quantum state, having the lowest energy. Hence, it is the analog for atoms of laser light for optics. Fifteen years having gone since its first experimental realization, BEC has proved to be a powerful tool to investigate a rich range of quantum processes, and a bridge between different fields of physics, such as atomics physics and condensed-matter physics. In this work, we will outline the history of BEC, which is made up of a large number of theoretical works and a lengthy experimental quest up to its final fulfilling. In addition, we will give an overview on the fertile research fields that BEC has allowed to explore, and the main perspectives opened by condensation of diluted atomic gases.