Various concepts related to smooth topological spaces have been introduced, and relations among them studied by several authors. In this paper we introduce the notions of smooth, quasi-smooth and weak smooth structure, showing that various properties of a smooth topological space can be expressed in terms of these structures. In particular, the definitions and the results of may be expressed in terms of the smooth and quasi-smooth structures. Then we will set out the fundamental concepts of these three structures and the relations between them.