  Based on some analogies with the Hodge theory of isolated hypersurface
singularities, we define Hodge-type numerical invariants (called H-numbers) of
any, not necessarily algebraic, link in $S^3$. They contain the same
information as the (normalized) real Seifert matrix. We study their basic
properties, we express the Tristram-Levine signatures and the higher order
Alexander polynomial in terms of them. Motivated by singularity theory, we also
introduce the spectrum of the link (determined from these H-numbers), and we
establish some semicontinuity properties for it.
