From the previous chapter, it is understood that one can study properties of Bose gases as well as quantum liquids more accurately in OPT rather than in Bilinear approximation. In the present chapter, we show that such an accurate investigation of BEC reveals its some “hidden” peculiarities leading to better predictions. In the practical application of OPT opens the way to the solution of Hohenberg-Martin dilemma [1] and describes the experimental data much better than the simple Bogolyubov approximation [2, 3]. In the next sections, we obtain the thermodynamic potential in OPT, outline the Hohenberg-Martin dilemma, and then show its possible solution. In the last sections, we shall calculate some physical observables, such as the condensate and superfluid densities, the static structure factor, etc.