  We present a general strong-coupling approach for the description of an
atomic Bose gas beyond the Bogoliubov approximation, when infrared divergences
start to occur that need to be resummed exactly. We consider the determination
of several important physical properties of the Bose gas, namely the chemical
potential, the contact, the speed of sound, the condensate density, the
effective interatomic interaction and the three-body recombination rate. It is
shown how the approach can be systematically improved with
renormalization-group methods and how it reduces to the Bogoliubov theory in
the weak-coupling limit.
