Contemporary astronomers continue to search for ways to understand the irregular distribution of galaxies in our Universe. This volume describes gravitational theory, computer simulations and observations related to galaxy distribution functions, which is a general method for measuring the distribution of galaxies and their motions. Coverage embeds distribution functions in a broader astronomical context, and includes other contemporary topics such as correlation functions, fractals, bound clusters, topology, percolation and minimal spanning trees. Throughout, theory, computer simulation and observation are carefully interwoven and critically compared, and key results are derived and the necessary gravitational physics provided. The book also shows how future observations can test the theoretical models for the evolution of galaxy clustering at early times in our Universe. This clear and authoritative volume is written at a level suitable for graduate students, and will be of key interest to astronomers, cosmologists, physicists and applied statisticians.