  An algebraic formulation of general relativity is proposed. The formulation
is applicable to quantum gravity and noncommutative space. To investigate
quantum gravity we develop the canonical formalism of operator geometry, after
reconstructing an algebraic canonical formulation on analytical dynamics. The
remarkable fact is that the constraint equation and evolution equation of the
gravitational system are algebraically unified. From the discussion of
regularization we find the quantum correction of the semi-classical gravity is
same as that already known in quantum field theory.
