  This article reviews recent investigations on the phenomenon of Bose-Einstein
condensation of dilute gases. Since the experimental observation of quantum
degeneracy in atomic gases, the research activity in the field of coherent
matter-waves literally exploded. The present topical review aims to give an
introduction into the thermodynamics of Bose-Einstein condensation, a general
overview over experimental techniques and investigations, and a theoretical
foundation for the description of bosonic many-body quantum systems.
