This theorem states that Every irreducible reduced crystallographic finite root system is isomorphic to exactly one of the following types: A n \ (n 1), B n \ (n 2), C n \ (n 3), D n \ (n 4), E 6,E 7,E 8,F 4,G 2.. It is used in the structure and classification of finite-dimensional Lie algebras, especially in arguments involving Cartan data, root systems, Weyl groups, and Dynkin diagrams.