In this chapter we will focus on the rules of aggregation hierarchies in analysis dimensions of a cube. We give an overview of the related works on the basic concepts of the different types of aggregation hierarchies. We then discuss the hierarchies from two different points of view: mapping between domain values and hierarchical structures. In relation to them, we introduce the characterization of some OLAP operators on hierarchies and give a set of operators that concern the change in the hierarchy structure. Finally, we propose an enlargement of the operator set concerning hierarchies.