  We employ the slice spectral sequence, the motivic Steenrod algebra, and
Voevodsky's solutions of the Milnor and Bloch-Kato conjectures to calculate the
hermitian $K$-groups of rings of integers in number fields. Moreover, we relate
the orders of these groups to special values of Dedekind $\zeta$-functions for
totally real abelian number fields. Our methods apply more readily to the
examples of algebraic $K$-theory and higher Witt-theory, and give a complete
set of invariants for quadratic forms over rings of integers in number fields.
