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Despite considerable research efforts on handling uncertainty in self-adaptive systems, a comprehensive understanding of the precise nature of uncertainty is still lacking. This paper summarises the findings of the 2023 Bertinoro Seminar on Uncertainty in Self- Adaptive Systems, which aimed at thoroughly investigating the notion of uncertainty, and outlining open challenges associated with its handling in self-adaptive systems. The seminar discussions were centered around five core topics: (1) agile end-toend handling of uncertainties in goal-oriented self-adaptive systems, (2) managing uncertainty risks for self-adaptive systems, (3) uncertainty propagation and interaction, (4) uncertainty in self-adaptive machine learning systems, and (5) human empowerment under uncertainty. Building on the insights from these discussions, we propose a research agenda listing key open challenges, and a possible way forward …