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We define a new class of racks, called finitely stable racks, which, to someextent, share various flavors with Abelian groups. Characterization of finitelystable Alexander quandles is established. Further, we study twisted rackdynamical systems, construct their cross-products, and introduce representationtheory of racks and quandles. We prove several results on the {\em strong}representations of finite connected involutive racks analogous to theproperties of finite Abelian groups. Finally, we define the {\em Pontryagin}dual of a rack as an Abelian group which, in the finite involutive connectedcase, coincides with the set of its strong irreducible representations.

Finitely stable racks and rack representations