The experimental realisation of Bose-Einstein condensates of dilute at
omic vapours has generated immense interest and activity in this field
. Here, we present a review of recent theoretical research into the pr
operties of trapped dilute-gas Bose-Einstein condensates. Topics cover
ed include ground-state properties of trapped condensates, elementary
excitations, light scattering properties, tests of broken gauge symmet
ry, and the atom laser. (C) 1998 Elsevier Science B.V. All rights rese
rved.