  We present a systematic and reliable methodology, termed hierarchical
mean-field theory (HMFT), to study and predict the behavior of strongly coupled
many-particle systems. HMFT is a simple approximation, based upon group
theoretical grounds, which deals with competing orders on an equal footing. It
is distinctly suitable when the various phases displayed by a system are the
result of competing interactions and non-linear couplings of their constituents
matter fields. We show applications relevant for systems implemented in optical
lattices.
