  The aim of this paper (Part III) is formulating GR as a scalar field theory.
The basic structural elements of it are a generating function, a generalized
density and a generalized temperature. One of the axioms of this theory is a
generalized Einstein equation which determines the generating function
directly. It is shown that basic concepts like orientation, time orientation
and isometry are expressible in terms of generating functions. At the end of
the paper six problems are formulated which are still unsolved and can act as a
stimulant for further research.
