Abstract: Since Newton in the Mathematical Principles of Nature Philosophy for the first time to define three body problem，people have been working on this problem for 300 years. At first，Euler and Lagrange studied some relatively simple three -body system problems. Poincaré first considered the restricted three -body problem，but found that its trajectory is too complex to be described. He turned to prove that there is no analytical solution for the three-body problem，and created a new subject，nonlinear dynamics.

Key words: three-body problem, Poincaré, nonlinear dynamics