Abstract
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.
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