  The renormalization group is not only a powerful method for describing
universal properties of phase transitions but it is also useful for evaluating
non- universal properties beyond mean-field theory. In this contribution we
concentrate on these latter aspects of the renormalization group approach. We
introduce its main underlying ideas in the familiar context of the ideal Bose
gas and then apply them to the case of an interacting, confined Bose gas within
the framework of the random phase approximation. We model confinement by
periodic boundary conditions and demonstrate how confinement modifies the flow
equations of the renormalization group changing thus the thermodynamic
properties of the gas.
