Though globally homogeneous, galaxies are unevenly distributed. This has been already known even before galaxies were recognized as extragalactic objects. Because of its random or stochastic nature, statistical characterization is the fundamental tool for quantifying the galaxy distribution in the Universe. The most basic statistical tool is the moment or cumulant-based measures, e.g., the n-point correlation function and polyspectrum. We introduce a systematic framework to formulate the correlation functions and polyspectra. The statistical tools developed here are not only important to quantitatively describe the galaxy distribution but also directly connected to the theoretical framework of structure formation in the Universe.