Type $${{\\varvec{D}}}_{{\\varvec{n}}}^\\mathbf{(1)}$$Dn(1) rigged configuration bijection

We establish a bijection between the set of rigged configurations and the set of tensor products of Kirillov---Reshetikhin crystals of type $$D^{(1)}_n$$Dn(1) in full generality. We prove the invariance of rigged configurations under the action of the combinatorial R-matrix on tensor products and show that the bijection preserves certain statistics (cocharge and energy). As a result, we establish the fermionic formula for type $$D_n^{(1)}$$Dn(1). In addition, we establish that the bijection is a classical crystal isomorphism.