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This tutorial paper summarizes the motivations, concepts and techniques of finite-set statistics (FISST), a system-level, “top-down,” direct generalization of ordinary single-sensor, single-target engineering statistics to the realm of multisensor, multitarget detection and tracking. Finite-set statistics provides powerful new conceptual and computational methods for dealing with multisensor-multitarget detection and tracking problems. The paper describes how “multitarget integro-differential calculus” is used to extend conventional single-sensor, single-target formal Bayesian motion and measurement modeling to general tracking problems. Given such models, the paper describes the Bayes-optimal approach to multisensor-multitarget detection and tracking: the multisensor-multitarget recursive Bayes filter. Finally, it describes how multitarget calculus is used to derive principled statistical approximations of this optimal filter, such as PHD filters, CPHD filters, and multi-Bernoulli filters.