The main objective of this Thesis is the construction of the fundamental modules of the classical Lie algebras. Weyl’s Theorem shows that if L is a semisimple Lie algebra, then any finite dimensional L−module is a direct sum of irreducible L−modules. Since the classical algebras are semisimple, we just need the irreducible modules in order to obtain the others. On the other hand, the fundamental modules give us every irreducible L− module and, therefore, every finite dimensional L−module.