  We define a new Gromov-Witten theory relative to simple normal crossing
divisors as a limit of Gromov-Witten theory of multi-root stacks. Several
structural properties are proved including relative quantum cohomology,
Givental formalism, Virasoro constraints (genus zero) and a partial
cohomological field theory. Furthermore, we use the degree zero part of the
relative quantum cohomology to provide an alternative mirror construction of
Gross-Siebert and to prove the Frobenius structure conjecture of
Gross-Hacking-Keel.
