The solution of the N-body problem is one of the oldest problems in science and it is most relevant even in today's physics for its applications to cosmology and astronomy. Leading mathematicians attacked this problem over more than three centuries without arriving at a definite answer. A central role is played by periodic or stable orbits with a particular emphasis on understanding gravity and how it operates among astronomical bodies, and their stability at all in the long run. Here the author organizes his presentation through a systematic study of the different possible configurations for...