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Such systems may operate as individual adaptive entities or as collective adaptive systems composed of multiple collaborating components. Rigorous engineering of these systems requires appropriate methods, models, and tools that ensure reliability, correctness, and alignment with their intended purpose. This paper introduces the first part of the special section on Rigorous Engineering of Collective Adaptive Systems. It presents six of the thirteen selected contributions and positions them within two major research directions: (i) Modelling and Engineering Collective Adaptive Systems, and (ii) Analysing Collective Adaptive Systems. 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