  The central principle of affine quantum gravity is securing and maintaining
the strict positivity of the matrix $\{\hg_{ab}(x)\}$ composed of the spatial
components of the local metric operator. On spectral grounds, canonical
commutation relations are incompatible with this principle, and they must be
replaced by noncanonical, affine commutation relations. Due to the partial
second-class nature of the quantum gravitational constraints, it is
advantageous to use the recently developed projection operator method, which
treats all quantum constraints on an equal footing. Using this method,
enforcement of regularized versions of the gravitational operator constraints
is formulated quite naturally by means of a novel and relatively well-defined
functional integral involving only the same set of variables that appears in
the usual classical formulation. It is anticipated that skills and insight to
study this formulation can be developed by studying special, reduced-variable
models that still retain some basic characteristics of gravity, specifically a
partial second-class constraint operator structure. Although perturbatively
nonrenormalizable, gravity may possibly be understood nonperturbatively from a
hard-core perspective that has proved valuable for specialized models. Finally,
developing a procedure to pass to the genuine physical Hilbert space involves
several interconnected steps that require careful coordination.
