  The principal aim of this article is to introduce and study n-valued quandles
and n-corack bialgebras. We elaborate the basic methods of this theory,
reproduce the coset construction known in the theory of n-valued groups. We
also consider a construction of n-valued quandles using n-multi-quandles. In
contrast to the case of n-valued groups this construction turns out to be quite
rich in algebraic and topological applications. An important part of the work
is the study of the properties of n-corack bialgebras those role is analogous
to the group bialgebra.
