For complex simple Lie algebras, the article provides the classification of all automorphisms of order 3. The method is an extension of Dynkin diagrams so that the classification is a listing of diagrams that represent automorphisms of order 3. This work extends an earlier result on automorphisms of order 2. As an application, it shows that for automorphisms of orders 2 and 3 only, the invariant subalgebra determines the automorphism.