this is the second volume in a series of books on the general theme of supersymmetric mechanics; the series is based on lectures and discussions held in 2005 and 2006 at the infn-laboratori nazionali di frascati. the first volume appears as lect. notes physics, vol. 698 supersymmetric mechanics , vol .1: supersymmetry, noncommutativity and matrix models (2006) isbn: 3-540-33313-4. the present extensive lecture supplies a pedagogical introduction, at the non-expert level, to the attractor mechanism in space-time singularities. in such a framework, supersymmetry seems to be related to dynamical systems with fixed points, describing the equilibrium state and the stability features of the thermodynamics of black holes. after a qualitative overview, explicit examples realizing the attractor mechanism are treated at some length; they include relevant cases of asymptotically flat, maximal and non-maximal, extended supergravities in 4 and 5 dimensions. a number of recent advances along various directions of research on the attractor mechanism are also given.