The book provides the most recent advances of Celestial Mechanics, as provided by high-level scientists working in this field. It covers theoretical investigations as well as applications to concrete problems. Outstanding review papers are included in the book and they introduce the reader to leading subjects, like the variational approaches to find periodic orbits, the stability theory of the N-body problem, the spin-orbit resonances and chaotic dynamics, the space debris polluting the circumterrestrial space.