Bose-Einstein condensation temperature of weakly interacting atoms

The critical temperature of Bose-Einstein condensation essentially depends on internal properties of the system as well as on the geometry of a trapping potential. The peculiarities of defining the phase transition temperature of Bose-Einstein condensation for different systems are reviewed, including homogenous Bose gas, trapped Bose atoms, and bosons in optical lattices. The method of self-similar approximants, convenient for calculating critical temperature, is briefly delineated.