In 1925 Einstein predicted that at low temperatures particles in a gas could all reside in the same quantum state. This gaseous state, a Bose-Einstein condensate, was produced in the laboratory for the first time in 1995 and investigating such condensates is one of the most active areas in contemporary physics. The authors of this graduate-level textbook explain this exciting new subject in terms of basic physical principles, without assuming detailed prior knowledge. Chapters cover the statistical physics of trapped gases, atomic properties, cooling and trapping atoms, interatomic interactions, structure of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. Problem sets are also included.