This paper represents the beginning of our final consideraticns of an approach to the foundations of mathematics initiated by the paper [5]. We shall deal in it with mathematical activity and its goals. We shall start from the assumption that the primary goal of mathematical activity is the creation of certain entities which will comprise in themselves (all) that activity. Such entities, we shall call mathematical entities. Our next assumption is that any performed mathematical activity creates conditions, i.e., makes a groundwork for a new mathematical activity and hence for the creation of new mathematical entities. These new entities ale of a higher level with respect to old ones. If we now assume that all mathematical entities constitute an edifice which we shall call the world of mathematics, then we shall have that this world consists of mathematical entities of various sorts and levels.