While these lectures are addressed firstly to theoreticians, anyway, the latters can not feel themselves fully happy without the satisfaction of their curiosity about the work of an experimenter. For this purpose, below we make a little excursion to experimenters. In the present book, we frequently use the phrase “Weakly interacting ultracold dilute Bose gases”. But the question arises, how a thermodynamic system can remain in the gaseous phase at very low temperatures instead of a crystal phase? The question is appropriate, since in accordance with typical \(P-T\) phase diagrams from textbooks, a stable equilibrium state of any gas (excluding, maybe hydrogen) should correspond to the crystal phase. This is true, for example, rubidium becomes solid already at \(T< 311\) K. Actually, it has been observed that any Bose condensed system of atoms has a very short lifetime. Soon after its creation, three-body recombination events (say, forces) lead to the formation of molecules, which eventually bring the BEC gas into the thermodynamic stable solid phase. Thus BEC phase is a metastable state! Moreover, it is not so easy to obtain even such a metastable state, otherwise, BEC could be created nearly 100 years ago, just after its theoretical prediction.