For statistics in probability theory, the Boolean-Poisson model or simply Boolean model for a random subset of the plane (or higher dimensions, analogously) is one of the simplest and most tractable models in stochastic geometry. Take a Poisson point process of rate \lambda in the plane and make each point be the center of a random set; the resulting union of overlapping sets is a realization of the Boolean model. More precisely, the parameters are \lambda and a probability distribution on compact sets; for each point \xi of the Poisson point process we pick a set C_\xi from the distribution, and then define as the union of translated sets. To illustrate tractability with one simple formula, the mean density of equals where \Gamma denotes the area of C_\xi and The classical theory of stochastic geometry develops many further formulae. As related topics, the case of constant-sized discs is the basic model of continuum percolation and the low-density Boolean models serve as a first-order approximations in the study of extremes in many models.