Bose-Einstein condensation of trapped atomic gases

This article reviews recent investigations on the phenomenon of Bose-Einste in condensation of dilute gases. Since the experimental observation of quan tum degeneracy in atomic gases, the research activity in the field of coher ent matter-waves literally exploded. The present topical review aims to giv e an introduction into the thermodynamics of Bose-Einstein condensation, a general overview over experimental techniques and investigations, and a the oretical foundation for the description of bosonic many-body quantum system s.