  This a brief introduction to the sequence of works \cite{KS:Kerr},
\cite{GKS-2022}, \cite{KS-GCM1}, \cite{KS-GCM2} and \cite{Shen} which establish
the nonlinear stability of Kerr black holes with small angular momentum. We are
delighted to dedicate this article to Demetrios Christodoulou for whom we both
have great admiration. The first author would also like to thank Demetrios for
the magic moments of friendship, discussions and collaboration he enjoyed
together with him.
