  Universal Lax pairs (the root type and the minimal type) are presented for
Calogero-Moser models based on simply laced root systems, including E_8. They
exist with and without spectral parameter and they work for all of the four
choices of potentials: the rational, trigonometric, hyperbolic and elliptic.
For the elliptic potential, the discrete symmetries of the simply laced models,
originating from the automorphism of the extended Dynkin diagrams, are combined
with the periodicity of the potential to derive a class of Calogero-Moser
models known as the `twisted non-simply laced models'. For untwisted non-simply
laced models, two kinds of root type Lax pairs (based on long roots and short
roots) are derived which contain independent coupling constants for the long
and short roots. The BC_n model contains three independent couplings, for the
long, middle and short roots. The G_2 model based on long roots exhibits a new
feature which deserves further study.
