  The notion of a Frobenius submanifold - a submanifold of a Frobenius manifold
which is itself a Frobenius manifold with respect to structures induced from
the original manifold - is studied. Two dimensional submanifolds are
particularly simple. More generally, sufficient conditions are given for a
submanifold to be a so-called natural submanifold. These ideas are illustrated
using examples of Frobenius manifolds constructed from Coxeter groups, and for
the Frobenius manifolds governing the quantum cohomology of CP^2 and CP^1
\times CP^1.
