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Published under the auspices of the Royal Astronomical Society, this volume contains a set of extensive school tested lectures, with the aim to give a coherent and thorough background knowledge of the subject and to introduce the latest developments in N-body computational astrophysics.§The topics cover a wide range from the classical few-body problem with discussions of resonance, chaos and stability to realistic modelling of star clusters as well as descriptions of codes, algorithms and special hardware for N-body simulations.§This collection of topics, related to the gravitational N-body problem, will prove useful to both students and researchers in years to come.