This text treats the Korteweg-de Vries (KdV) equation with periodic boundary conditions. This equation models waves in homogeneous, weakly nonlinear and weakly dispersive media in general. For the first time, these important results are comprehensively covered in book form, authored by internationally renowned experts in the field.

I The Beginning.- II Classical Background.- III Birkhoff Coordinates.- IV Perturbed KdV Equations.- V The KAM Proof.- VI Kuksin's Lemma.- VII Background Material.- VIII Psi-Functions and Frequencies.- IX Birkhoff Normal Forms.- X Some Technicalities.- References.- Notations.