  We introduce a new class of integral domains, the perinormal domains, which
fall strictly between Krull domains and weakly normal domains. We establish
basic properties of the class, and in the case of universally catenary domains
we give equivalent characterizations of perinormality. (Later on, we point out
some subtleties that occur only in the non-Noetherian context.) We also
introduce and explore briefly the related concept of global perinormality,
including a relationship with divisor class groups. Throughout, we provide
illuminating examples from algebra, geometry, and number theory.
