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.

Periodic Orbits and Variational Methods.- On the variational approach to the periodic n-body problem.- On families of periodic solutions of the restricted three-body problem.- Hip-hop solutions of the 2N-body problem.- Double choreographical solutions for n-body type problems.- From the circular to the spatial elliptic restricted three-body problem.- Stability of axial orbits in galactic potentials.- Perturbation Theory and Regularization.- KAM tori for N-body problems: a brief history.- Analysis of the chaotic behaviour of orbits diffusing along the Arnold web.- The scattering map in the planar restricted three body problem.- On final evolutions in the restricted planar parabolic three-body problem.- Quaternions and the perturbed Kepler problem.- Dynamics of Solar and Extrasolar Systems.- The 3:2 spin-orbit resonant motion of Mercury.- Symmetric and asymmetric librations in extrasolar planetary systems: a global view.- The influence of mutual perturbations on the eccentricity excitation by jet acceleration in extrasolar planetary systems.- Symmetric and asymmetric 3:1 resonant periodic orbits with an application to the 55Cnc extra-solar system.- Estimations of orbital parameters of exoplanets from transit photometry by using dynamical constraints.- Critical inclination in the main problem of a massive satellite.- Long-term effects of the Galactic tide on cometary dynamics.- Dependence on the observational time intervals and domain of convergence of orbital determination methods.- Space Dynamics and Applications.- Collision risk against space debris in Earth orbits.- On target for Venus - set oriented computation of energy efficient low thrust trajectories.- Weak stability boundary trajectories for the deployment of lunar spacecraft constellations.- Aero-gravityassist maneuvers: controlled dynamics modeling and optimization.- Analytical theory of a lunar artificial satellite with third body perturbations.- Precise measurement of the solar gravitational red shift.