  We describe a novel method which allows the treatment of high orders of
replica-symmetry-breaking (RSB) at low temperatures as well as at T=0 directly,
without a need for approximations or scaling assumptions. It yields the low
temperature order function q(a,T) in the full range $0\leq a <\infty$ and is
complete in the sense that all observables can be calculated from it. The
behavior of some observables and the finite RSB theory itself is analyzed as
one approaches continuous RSB. The validity and applicability of the
traditional continuous formulation is then scrutinized and a new continuous RSB
formulation is proposed.
