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Replicability is vital to ensuring scientific conclusions are reliable, but failures of replicability have been a major issue in nearly all scientific areas of study, and machine learning is no exception. In this course, we will study replicability as a property of learning and other statistical algorithms, developing a theory of replicable learning. We will cover recent formalizations of replicability and their relationships to other common stability notions such as differential privacy and adaptive generalization. We will survey replicable algorithms for fundamental learning tasks, and discuss the limitations of replicable algorithms. If time permits, we will discuss replicability in other settings, such as reinforcement learning and clustering, or other useful and related stability notions such as list replicability and global stability. Required Course Background: EN.601.433/633 Intro Algorithms or instructor permission.