  Chaos as typical property of non-linear systems has revealed its crucial role
in various problems of astrophysics and cosmology. The problems discussed at
these lectures include planetary dynamics, galactic dynamics, reconstruction of
the substructure of clusters of galaxies, instability in Wheeler-DeWitt
superspace. The choice of the problems aimed to show also the diversity of
approaches and mathematical tools, which include the geometric criterion
(Ricci) of relative instability in many dimensional systems, the estimation of
Kolmogorov-Sinai entropy, the hyperbolicity in pseudo-Riemannian spaces, etc.
