The classification program of Elliott, the goal of which is to classify amenable C*-algebras by their K-theoretical data, has been successful for many classes of C*-algebras, in particular for simple AH algebras with no dimension growth. Therefore, the AH algebras which may be most interested in nowadays are the one with higher dimension growth (than zero). In this talk, we will study dimension theory (stable rank and real rank) of simple AH-algebras (the algebras can be written as inductive limits of matrices algebras over commutative C*-algebras). In particular, we are interested in the algebras which can be written as inductive limits of commutative C*-algebras with ”diagonal connecting maps” but without any hypothesis on dimension. This class include interesting algebras: AF algebras, AI and AT algebras, Goodearl algebras, algebras constructed by Villadsen, and, by Toms.