  We present in detail a new systematic method which can be used to
automatically eliminate the renormalization scheme and scale ambiguities in
perturbative QCD predictions at all orders. We show that all of the
nonconformal \beta-dependent terms in a QCD perturbative series can be readily
identified by generalizing the conventional renormalization schemes based on
dimensional regularization. We then demonstrate that the nonconformal series of
pQCD at any order can be resummed systematically into the scale of the QCD
coupling in a unique and unambiguous way due to a special degeneracy of the
\beta-terms in the series. The resummation follows from the principal of
maximum conformality (PMC) and assigns a unique scale for the running coupling
at each perturbative order. The final result is independent of the initial
choices of renormalization scheme and scale, in accordance with the principles
of the renormalization group, and thus eliminates an unnecessary source of
systematic error in physical predictions. We exhibit several examples known to
order \alpha_s^4; i.e. i) the electron-positron annihilation into hadrons, ii)
the tau-lepton decay to hadrons, iii) the Bjorken and Gross-Llewellyn Smith
(GLS) sum rules, and iv) the static quark potential. We show that the final
series of the first three cases are all given in terms of the anomalous
dimension of the gluon field, in accordance with conformality, and with all
non-conformal properties encoded in the running coupling. The final expressions
for the Bjorken and GLS sum rules directly lead to the generalized Crewther
relations, exposing another relevant feature of conformality. The static quark
potential shows that PMC scale setting in the Abelian limit is to all orders
consistent with QED scale setting. Finally, we demonstrate that the method
applies to any renormalization scheme and [...]
