In general, the phase space of a completely integrable Hamiltonian
System (HS) of n degrees of freedom is foliated by invariant
n-dimensional tori on which the motion is quasi-periodic.
Kolmogorov-Arnold-Moser (KAM) theory deals with persistence, under
(hamiltonian) perturbation, of (the majority of) such tori.
Starting from the late eighties KAM Theory was applied to infinite
dimensional HS, e.g. to PDEs with Hamiltonian structure.
While the Theory for finite dimensional tori is well established, very
few results are know for infinite dimensional tori supporting
almost-periodic solutions. I will discuss some recents developments on
the subject, obtained in collaboration with J. Massetti and M. Procesi.