This book provides a brief introduction to some basic but important problems in celestial mechanics, and particularly in the few-body problem, such as the permissible and forbidden region of motion, the evolution of moment of inertia of a system, and the orbital stability of asteroids in the solar system. All these are based on some main results in the authors' research works, which are related to the qualitative method of celestial mechanics and nonlinear dynamics. Some of these works are interdisciplinary, involving celestial mechanics, nonlinear dynamics and other disciplines. The book covers a variety of topics for dynamics in the solar system, including the comets, asteroids, planetary rings, Trojan asteroids, etc.As a senior scientist, Professor Sun shares his research experiences in this book. Readers may find plenty of information both about the theoretical and numerical analyses in celestial mechanics, and about the applications of theories and methods to dynamical problems in astronomy.