This book gives a detailed analysis of earthquake clustering as the realization of a point process modelled by a generalized Poisson distribution. No hypothesis is inferred on the physical model of such a process. The occurrence of a seismic event within an infinitesimal volume of the space of its characterizing parameters is supposed to be completely random; while the behavior in a reasonably large volume of the same space may exhibit some average non-random features. The description of seismicity as a point process in space, time and magnitude is suitable for the application of statistical tools for comparing the performance of different models. Examples of application of such algorithms to real seismicity are included.