We define an invariant called the “commutative differential graded algebra with lattice” of a topological space X. The commutative differential graded algebra with lattice encodes the information of rational homotopy type of X and the “lattice structure of X”. We compute the quasi-isomorphism classes of several commutative differential graded algebra with lattices. Moreover, we define an integral Sullivan model. And we prove that, under some conditions, a commutative differential graded algebra with lattice has an integral Sullivan model. i