2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55964We summarize recent results on the construction of Lax pairs with spectral parameter for the twisted and untwisted elliptic Calogero-Moser systems associated with arbitrary simple Lie algebras, their scaling limits to Toda systems, and their role in Seiberg-Witten theory. We extend part of this work by presenting a new parametrization for the spectral curves for elliptic spin Calogero-Moser systems associated with SL(N).18 pages, no figures, Plain TeX; Contribution to "Regular and Chaotic Dynamics" dedicated to J. Moser; several references addedHigh Energy Physics - TheoryExactly Solvable and Integrable Systemstext