SEPARATION OF VARIABLES - NEW TRENDS

The review is based on the author's papers since 1985 in which a new a pproach to the separation of variables (SoV) has being developed. It i s argued that SoV, understood generally enough, could be the most univ ersal tool to solve integrable models of the classical and quantum mec hanics. It is shown that the standard construction of the action-angle variables from the poles of the Baker-Akhiezer function can be interp reted as a variant of SoV, and moreover, for many particular models it has a direct quantum counterpart. The list of the models discussed in cludes XXX and XYZ magnets, Gaudin model, Nonlinear Schrodinger equati on, SL(3)-invariant magnetic chain. New results for the 3-particle qua ntum Calogero-Moser system are reported.