The problem of the invariant classification of the orthogonal coordinate webs
defined in Euclidean space is solved within the framework of Felix Klein's
Erlangen Program. The results are applied to the problem of integrability of
the Calogero-Moser model.
Subjects: Mathematical Physics; Astrophysics; Mathematics - Analysis of PDEs; Mathematics - Differential Geometry; Nonlinear Sciences - Exactly Solvable and Integrable Systems