  To a pair $P$ and $Q$ of finite posets we attach the toric ring $K[P,Q]$
whose generators are in bijection to the isotone maps from $P$ to $Q$. This
class of algebras, called isotonian, are natural generalizations of the
so-called Hibi rings. We determine the Krull dimension of these algebras and
for particular classes of posets $P$ and $Q$ we show that $K[P,Q]$ is normal
and that their defining ideal admits a quadratic Gr\"obner basis.
