I will give an overview of the N-Body method with an emphasis on collisionless systems and the multiscale methods that allow us to resolve a large dynamic range. In this context I will discuss two challenging problems: (i) The gravitational collapse and virialisation of a density perturbation and (ii) the merging of two galaxies with central supermassive black holes. The former problem is remarkable since nearly all initial conditions tend to the same final state. The latter problem requires us to follow interactions between a collisional component (binary black holes) and a collisionless background of stars and dark matter over a dynamical range of 10^8.
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