  The theory of representations of quivers and of their preprojective algebras
are reviewed. In particular, moduli spaces of representations of these
algebras, quiver varieties and reflection functor are described. The proof that
the bijection between moduli spaces induced by the reflection functor is an
isomorphism of symplectic affine varieties is presented. Hamiltonian systems
with complete flows on the quiver varieties are introduced. An application of
the reflection functor to these systems is described. The results on the case
of the cyclic quiver are reviewed and a role of the reflection functor in this
case is discussed. In particular, "spin" integrable generalisations of the
Calogero-Moser systems and their application to the generalised KP hierarchies
are considered.
