  We construct relative Gromov--Witten theory with expanded degenerations in
the normal crossings setting and establish a degeneration formula for the
resulting invariants. Given a simple normal crossings pair $(X,D)$, we show
that there exist proper moduli spaces of curves in $X$ with prescribed boundary
conditions along $D$, equipped with virtual classes. Each point in such a
moduli space parameterizes a map from a nodal curve to an expanded degeneration
of $X$ that is dimensionally transverse to the strata. In the context of maps
to a simple normal crossings degeneration, the virtual fundamental class is
known to decompose as a sum over tropical maps. We use the expanded formalism
to prove the degeneration formula -- we reconstruct the virtual class attached
to a tropical map in terms of spaces of maps to expansions attached to the
vertices.

Algebraic Geometry