  We propose and study the following Mirror Principle: certain sequences of
multiplicative equivariant characteristic classes on Kontsevich's stable map
moduli spaces can be computed in terms of certain hypergeometric type classes.
As applications, we compute the equivariant Euler classes of obstruction
bundles induced by any concavex bundles -- including any direct sum of line
bundles -- on $\P^n$. This includes proving the formula of Candelas-de la
Ossa-Green-Parkes hence completing the program of Candelas et al, Kontesevich,
Manin, and Givental, to compute rigorously the instanton prepotential function
for the quintic in $\P^4$. We derive, among many other examples, the multiple
cover formula for Gromov-Witten invariants of $\P^1$, computed earlier by
Morrison-Aspinwall and by Manin in different approaches. We also prove a
formula for enumerating Euler classes which arise in the so-called local mirror
symmetry for some noncompact Calabi-Yau manifolds. At the end we interprete an
infinite dimensional transformation group, called the mirror group, acting on
Euler data, as a certain duality group of the linear sigma model.
