  These notes present simple theoretical approaches to study Bose-Einstein
condensation in trapped atomic gases and their comparison to recent
experimental results : - the ideal Bose gas model - Fermi pseudopotential to
model the atomic interaction potential - finite temperature Hartree-Fock
approximation - Gross-Pitaevskii equation for the condensate wavefunction -
what we learn from a linearization of the Gross-Pitaevskii equation -
Bogoliubov approach and thermodynamical stability - phase coherence properties
of Bose-Einstein condensates - symmetry breaking description of condensates
