  $SU(\infty)$-QGR is a quantum approach to Universe and gravity. Its main
assumption is infinite mutually commuting observables in the Universe, leading
to representation of $SU(\infty)$ by its Hilbert spaces and those of its
subsystems. The Universe as a whole is static, topological, and characterized
by two continuous parameters. Nonetheless, quantum fluctuations induce
clustering and finite rank internal symmetries, which approximately divide the
Universe to infinite interacting subsystems. Their Hilbert space depends on an
additional dimensionful parameter, and selection of a subsystem as clock
induces a relative dynamics, with $SU(\infty)$ sector as gravity. The
Lagrangian defined on the (3+1)-dimensional parameter space is Yang-Mills for
both symmetries. When quantumness of gravity is undetectable, it is perceived
as curvature of an effective spacetime.
