The Kepler problem. History and theory (Q2856000)

Johannes Kepler discovered empirically (in 1609 and 1618) the laws of motion of planets around the Sun and tried to provide the formal foundation of them. This problem was solved after Newton stated his laws of mechanics (in \textit{Principia}, 1687). But many mathematicians looked in the following after some new understandings to the problem within the framework of other theories such as Lagrangian mechanics, or Hamiltonian mechanics, or (even) quantum mechanics. The book under review gives an excellent survey of various ideas and results on the subject that appeared between 1609 and 2010. It consists of three chapters: History, Theory, (Mathematical) Appendix, and an extensive bibliography (more than 100 items).