  We build the abstract theory of Gromov-Witten invariants of genus 0 for
quantum minimal Fano varieties (a minimal natural (with respect to
Gromov-Witten theory) class of varieties). In particular, we consider ``the
minimal Gromov-Witten ring'', i. e. a commutative algebra with generators and
relations of the form used in the Gromov-Witten theory of Fano variety (of
unspecified dimension). Gromov-Witten theory of any quantum minimal variety is
a homomorphism of this ring to $\mathbb C$. We prove the Abstract
Reconstruction Theorem which states the particular isomorphism of this ring
with a free commutative ring generated by ``prime two-pointed invariants''. We
also find the solutions of the differential equations of type DN for a Fano
variety of dimension N in terms of generating series of one-pointed
Gromov-Witten invariants.
