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This article is a tutorial on advanced automated processalgebraic verification of concurrent systems, and it is organised around a case study. The emphasis is on verification methods that rely on the inherent compositionality of process algebras. The fundamental concepts of labelled transition systems, strong bisimilarity, synchronous parallel composition, hiding, renaming, abstraction, CFFD-equivalence and CFFD-preorder are presented as the case study proceeds. The necessity of presenting assumptions about the users of the example system is discussed, and it is shown how CFFD-preorder supports their modelling. The assumptions are essential for the verification of so-called liveness properties. The correctness requirements of the system are stated, presented in linear temporal logic, and distributed to a number of more "localised" requirements. It is shown how they can be checked with the aid of suitably chosen CFFD-abstracted views to the system. The state explosion problem that hampers automatic verification is encountered. Compositional LTS construction, interface specifications and induction are used to solve the problem and, as a result, an infinite family of systems is verified with a limited amount of effort.