  To a natural number $n$, a finite partially ordered set $P$ and a poset ideal
${\mathcal J}$ in the poset $Hom(P,[n])$ of isotonian maps from $P$ to the
chain on $n$ elements, we associate two monomial ideals, the letterplace ideal
$L(n,P;{\mathcal J})$ and the co-letterplace ideal $L(P,n;{\mathcal J})$. These
ideals give a unified understanding of a number of ideals studied in monomial
ideal theory in recent years. By cutting down these ideals by regular sequences
of variable differences we obtain: multichain ideals and generalized Hibi type
ideals, initial ideals of determinantal ideals, strongly stable ideals,
$d$-partite $d$-uniform ideals, Ferrers ideals, edge ideals of cointerval
$d$-hypergraphs, and uniform face ideals.
