  The work of Kolmogorov, Arnold and Moser appeared just before the
renormalization group approach to statistical mechanics was proposed by Wilson:
it can be classified as a multiscale approach which also appeared in works on
the convergence of Fourier's series, or construction of Euclidean quantum
fields, or the scaling analysis of the short scale behaviour of Navier-Stokes
fluids to name a few which originated a great variety of further problems. In
this review the proof of the KAM theorem will be presented as a classical
renormalization problem with the harmonic oscillator as a `trivial' fixed
point.
