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This paper is based on three tutorial lectures given at the CRM Summer Schoolin Banff, Alberta, June 27-July 10, 1999 on "Theoretical Physics at the End ofthe Twentieth Century". They will be published by Springer-Verlag. Lecture Igives a quick overview of recent studies of BEC in trapped atomic gases andreviews some properties of a trapped non-interacting Bose gas. Lecture IImainly discusses the collective modes of a pure condensate, based on the T=0 GPequation of motion. The Stringari quantum hydrodynamic theory is introduced.Lecture III discusses the coupled dynamics of the condensate and non-condensateat finite temperatures. A recent derivation of the two-fluid hydrodynamicequations is sketched. This theory predicts a new relaxational mode associatedwith the fact that the condensate and non-condensate may not be in diffusiveequilibrium.

BEC and the New World of Coherent Matter Waves