This symposium was devoted to a new celestial mechanics whose aim has become the study of such "objects" as the planetary system, planetary rings, the asteroidal belt, meteor swarms, satellite systems, comet families, the zodiacal cloud, the preplanetary nebula and more. Looking at the three-body problem, instead of individual orbits, the text considers the topology of extended regions of its phase space. This symposium was one step in the effort to close the ties between two scientific families: the observationally-oriented scientists and the theoretically-oriented scientists.