This very complete monograph, written by renowned experts in the field, is a graduate-level introduction to Bose-Einstein Condensation. Topics covered include the history of BEC, quantum field theory of quantum gases, the Bogoliubov theory, condensate wavefunction and the Gross-Pitaevskii equation, vortices and solitons, the excitation spectrum, phase space methods for bosonic systems, quantum theory of coherence and fluctuations in a BEC, irreveribility, and damping.