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This lecture by the instructor covers the topic of safe learning in robotics, focusing on the state of the art, enabling progress, open challenges, and vision in the field. The lecture discusses the safe learning control problem, types of safety guarantees, and approaches to encouraging safety and robustness in reinforcement learning. It also explores certifying learning-based control and constraint set certification. The presentation includes key features of safe-control-gym, current controllers, results on constraint satisfaction, performance, and data efficiency, as well as the IROS 2022 Safe Robot Learning Competition. The lecture concludes with a summary of the challenges in the field and the importance of interdisciplinary collaboration for safe robot autonomy research.