Brief introduction to the nonlinear stability of Kerr

This a brief introduction to the sequence of works [65], [41], [63], [64] and[85] 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.