In Chapter 5, we consider the BEC-BCS crossover problem in the dilute atomic gases frm a general point of view. We show that as a result of the specific properties of the ultra-cold Fermi gases, there exists a universal function which incorporates all the many-body information of the system. Although we do not yet know how to compute the function analytically, we show that many physical quantities can be expressed in terms of this function. It gives an intuitive way of understanding of how universality arises in the cold atomic gases.