  Let $\mathfrak{g}$ be a complex semisimple Lie algebra. We give a
classification of contravariant forms on the nondegenerate Whittaker
$\mathfrak{g}$-modules $Y(\chi, \eta)$ introduced by Kostant. We prove that the
set of all contravariant forms on $Y(\chi, \eta)$ forms a vector space whose
dimension is given by the cardinality of the Weyl group of $\mathfrak{g}$. We
also describe a procedure for parabolically inducing contravariant forms. As a
corollary, we deduce the existence of the Shapovalov form on a Verma module,
and provide a formula for the dimension of the space of contravariant forms on
the degenerate Whittaker modules $M(\chi, \eta)$ introduced by McDowell.
