The N-Body Problem is the mathematical/dynamical problem of describing the course of multiple celestial bodies interacting via Gravity. The Two-Body problem can be solved analytically. Three or more bodies can be addressed with a Taylor Series or through N-Body Simulation, i.e., calculating the motions in small steps.
In some cases, e.g., multiple planets orbiting a star, some generalized information can be calculated such as whether the orbits are likely to remain stable (a planet thrown out of the system would imply instability, for example) or become chaotic, i.e., Perturbation Theory. The Jacobi Integral is another method addressing Three Body Problems.
Adaptive Refinement Tree (ART)