  We consider the theory of Lax equations in complex simple and reductive
classical Lie algebras with the spectral parameter on a Riemann surface of
finite genus. Our approach is based on the new objects -- the Lax operator
algebras, and develops the approach of I.Krichever treating the $\gl(n)$ case.
For every Lax operator considered as the mapping sending a point of the
cotangent bundle on the space of extended Tyrin data to an element of the
corresponding Lax operator algebra we construct the hierarchy of mutually
commuting flows given by Lax equations and prove that those are Hamiltonian
with respect to the Krichever-Phong symplectic structure. The corresponding
Hamiltonians give integrable finite-dimensional Hitchin-type systems. For
example we derive elliptic $A_n$, $C_n$, $D_n$ Calogero-Moser systems in frame
of our approach.
