This grant supports research that will contribute to the advancement of national prosperity and social and economic welfare by developing adaptive control and learning algorithms to solve complex, practical problems arising from networked systems with uncertainties. Large-scale service operations, manufacturing and production systems, inventory and logistics, healthcare patient flows, telecommunications, and cloud computing all have complex network structures and often face various challenging operational risks such as sudden changes in demand or disruptions in service. Unlike traditional methods that assume full knowledge of system behavior, this research will create new algorithms that can learn from data and adapt in real time, while also accounting for risk and variability in outcomes - weighing in on the potentially high fluctuations around the average values of certain performance metrics. Beyond the technical contributions, the project will enhance STEM education by integrating cutting-edge research into both undergraduate and graduate curricula. It will prepare students with advanced mathematical and engineering skills needed to lead in fields like artificial intelligence, operations research, industrial and systems engineering - strengthening the U.S. science and engineering workforce. This research will advance the computational and learning methods of risk-sensitive control of Markov chains and diffusions and their applications in stochastic networked systems.