Publisher Summary This chapter presents the quotient cube as a succinct summary of a data cube lattice, preserving its rollup–drilldown semantics. It gives a quick and concise summary to the user, based on which they may decide to explore different regions of the cube. Quotient cubes are based on partitions on the cube lattice and this chapter characterizes those partitions that lead to a reduced lattice structure. Monotone aggregate functions yield a unique maximal convex partition while non-monotone ones do not. The algorithms significantly outperform the previously proposed MinCube algorithm. Designing scalable algorithms for quotient cube for AVG is important. Partitioning a data cube into sets of cells with “similar behavior” often better exposes the semantics in the cube. The data cube is one of the most influential operators in online analytical processing (OLAP). It is instructive to classify works on issues surrounding it into two “generations.” In the first generation, the main focus is to devise efficient algorithms for computing the cube—the full cube from scratch, choosing views to materialize under space constraints, handling sparsity, cube compression, approximation, and computing the cube under user-specified constraints. In the second generation, researchers focus on extracting more “semantics” from a data cube.