  This is the first in a series of papers, in which we compute the third-order
QCD corrections to top-antitop production near threshold in e+ e- collisions.
The present paper provides a detailed outline of the strategy of computation in
the framework of non-relativistic effective theory and the threshold expansion,
applicable more generally to heavy-quark pair production near threshold. It
summarizes matching coefficients and potentials relevant to the
next-to-next-to-next-to-leading order and ends with the master formula for the
computation of the third-order Green function. The master formula is evaluated
in part II of the series.
