The development of quantum theory of gases is reviewed from the end of XIX century up to nowadays. Especcially the contribution of S. Bose and Einstein to the theory of quantum gases is considered. Bose-Einstein, Fermi-Dirac, intermediate statistics, and Bose-Einstein condensation are briefly discussed. After short consideration the phenomenon of laser cooling the contribution of Nobel laureates in physics for 2001 in the problem of achieving Bose-Einstein condensation in alkali gases is described.