Perturbation theory
In applications, one can rarely sum exactly the Magnus series, and one has to truncate it to get approximate solutions. The main advantage of the Magnus proposal is that the truncated series very often shares important qualitative properties with the exact solution, at variance with other conventional [[Perturbation theory|perturbation]] theories. For instance, in [[classical mechanics]] the [[Symplectic geometry|symplectic]] character of the [[time evolution]] is preserved at every order of approximation. Similarly, the [[unitary operator|unitary]] character of the time evolution operator in [[quantum mechanics]] is also preserved (in contrast, e.g., to the [[Dyson series]] solving the same problem).