  We give an explicit description of the lattice $\Semistar(D)$ of all semistar
operations on any Dedekind domain $D$ from its set $\Max(D)$ of maximal ideals.
This descpription is constructive if $\Max(D)$ is finite. As a corollary we
show that $2^{{n \choose [n/2]}} \leq |\Semistar(D)| \leq 2^{2^n}$ if $n =
|\Max(D)|$ is finite; we compute $|\Semistar(D)|$ if $|\Max(D)| \leq 7$; and we
show that if $\Max(D)$ is infinite then $\Semistar(D)$ has cardinality
$2^{2^{|\Max(D)|}}$.
