Abstract link diagrams and virtual knots

The notion of an abstract link diagram is re-introduced with a relationship with Kauffman's virtual knot theory. It is proved that there is a bijectio n from the equivalence classes of virtual link diagrams to those of abstrac t link diagrams. Using abstract link diagrams, we have a geometric interpre tation of the group and the quandle of a virtual knot. A generalization to higher dimensional cases is introduced, and the state-sum invariants are tr eated.