This article is a very clear introduction in the subject. For my opinion it will be nice to include a brief references on applications of the Calogero-Moser systems in theoretical physics (Quantum Hall Effect, SUSY Yang-Mills theory) and in mathematics (affine Hecke algebras, Representation theory)
This article is an excellent introduction to the various subjects covered by or overlapping with the Calogero-Moser System. However, the author might be willing to take care of the following suggestions:
1. When he writes
"Another line of generalization has associated internal degrees of freedom ("spin") to the particles whose time evolution is described by CM-type models"
One could add something sounding as:
"In this respect, it is remarkable that, by the so called "freezing trick" introduced by A.Polychronakos, one has been able to establish a connection by the quantum Calogero-Moser system with spin in the large coupling limit (\(a\to \infty\)) and celebrated spin-chains models of the Haldane-Shastri type"
2. Always about the extensions, it could be worth mentioning the available results on the exact time-discretization of Calogero-Moser type models (Rauch-Wojciechowski, 1983; Nijhoff-Pang, Nijhoff-Kuznetsov-Ragnisco, 1996-7, Suris (book on integrable discretizations)) and their connections with Bethe ansatz approach to spin chains.
The article is very well-written and clear and it is going to be an excellent introduction to the topic. I only corrected very few minor typos. Please, note the comment that I have incorporated within the text.