  The integrability of the classical and quantum rational Calogero-Moser
systems is verified explicitly via the Lax pair method for the case $n=3$. We
provide an extensive survey of reflection groups and root systems. The
Olshanetsky-Perelomov operators are constructed for a general root system via
Dunkl operators, associated to root systems. The integrability of the quantum
rational Calogero-Moser system is discussed via the Olshanetsky-Perelomov
operators, which provide a set of commuting integrals of motion. The classical
analogues of both the Dunkl and the Olshanetsky-Perelomov operators are also
presented.
