  This Tutorial is the continuation of the previous tutorial part, published in
Laser Phys. 23, 062001 (2013), where the basic mathematical techniques required
for an accurate description of cold atoms for both types of quantum statistics
are expounded. In the present part, the specifics of the correct theoretical
description of atoms obeying Bose-Einstein statistics are explained, including
trapped Bose atoms. In the theory of systems exhibiting the phenomenon of
Bose-Einstein condensation, there exists a number of delicate mathematical
points, whose misunderstanding often results in principally wrong conclusions.
This is why the consideration in the present Tutorial is sufficiently detailed
in order that the reader could clearly understand the underlying mathematics
and would avoid confusions.

Quantum Gases