  A manifestly gauge invariant continuous renormalization group flow equation
is constructed for pure SU(N) gauge theory. The formulation makes sense without
gauge fixing and manifestly gauge invariant calculations may thus be carried
out. The flow equation is naturally expressed in terms of fluctuating Wilson
loops, with the effective action appearing as an integral over a `gas' of
Wilson loops. At infinite N, the effective action collapses to a path integral
over the trajectory of a single particle describing one Wilson loop. We show
that further regularization of these flow equations is needed. (This is
introduced in part II.)
