Our group in Trento has been involved in the physics of quantum fluids for many years, and before 1999 we had already published several successful papers on the physics of trapped Bose-Einstein condensates. It became natural for us to make the effort to provide this comprehensive review.

It contributed by clarifying some important features emerging from the experimental activities within a self-consistent theoretical scheme and it helped to identify the most significant novel developments. The field of cold atoms is rather interdisciplinary and represents a sort of crossroads for people working in different areas (atomic physics, condensed matter, low temperature, quantum optics, etc.), so that a review paper is also useful to settle a common conceptual background.

The number of laboratories involved in experiments on cold atoms and Bose-Einstein condensates is growing in an impressive way. Most of the subjects that we listed in the "outlook" section of our paper have already been explored and many novel topics are now becoming the object of new experimental and theoretical investigations. Among them are the occurrence of new quantum phases, the realization of periodic structures with condensates in optical lattices, and the investigation of quantum gases in one and two dimensions. There is now a wider variety of atomic species that are cooled and condensed in both magnetic and optical traps. Moreover, an entirely new field of research has been opened by the most recent experiments with cold fermions, Feshbach resonances, and molecular condensates. Promising perspectives for the future concern the use of Bose-Einstein condensates for atom interferometry and for quantum information studies.

We believe that the experimental and theoretical work of these years on Bose-Einstein condensation will be recognized as a key advance in atomic and in quantum statistical physics.