**4d gauge theories and classical integrable systems**

**Abstract:**

A wide class of integrable classical systems
(the so-called Hitchin systems) can be
derived from a topological field theory in 2+1 dim.
They include, in particular, the Calogero-Moser systems, the Toda models,
integrable tops, the KdV equation, the Landau-Lifshitz equation. This
approach
allows to obtain immediately the Lax equations with a spectral parameter
and
the conservation laws.
I plan to explain the general theory and then to illustrate it by two
examples:

1. Elliptic Calogero-Moser systems

2. Elliptic tops

Then I establish an equivalence of these systems and explain, follow
Kapustin-Witten, how this equivalence can be explain in the framework
of 4-d topological theory by a presence of a monopole.