  Given a compact K\"ahler manifold, the Infinitesimal Torelli problem asks
whether the differential of the period map of a Kuranishi family is injective.
Unlike the classical Torelli theorem for curves, there is a negative answer for
example for hyperelliptic curves of genus greater than $2$. Nevertheless the
Infinitesimal Torelli Theorem holds for many other classes of manifolds. We
will prove it for smooth hypersurfaces in simple abelian varieties with
sufficiently high self-intersection giving an effective bound on a result by
Green in this particular case.
