KAM for PDEs

In the last years much progress has been achieved in the theory of quasi-periodic solutions of PDEs, that we shall call in a broad sense “KAM theory for PDEs”. Many new tools and ideas have been developed in this field (and are in current progress) establishing new links with other areas of dynamical systems (like normal forms) and PDE analysis (like micro-local analysis). We provide an overview to the state of the art in KAM theory for PDEs. © 2016 Unione Matematica Italiana.