We review the algebraic Bethe ansatz for the Heisenberg model. The exposition includes some of recent advancements with emphasis on a relation with the rigged configurations. We also provide somewhat thorough review of the crystal bases and the rigged configurations. In particular, we provide the inverse scattering transform for the type $D^{ (1)}_n$ box-ball systems. We also provide a reformulation of a result of arXiv:0711.4185.
Categories: math.QA math-ph math.MP