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This lecture covers the concept of subtyping in programming languages, focusing on the rules and relations between different types. It explains how subtyping allows for more flexible and expressive type systems, showcasing examples with records, arrays, and references. The lecture also delves into the challenges of non-syntax-directed subtyping and the importance of algorithmic relations. Additionally, it discusses the connection between subtyping and polymorphism, highlighting the various forms of polymorphism such as parametric, subtype, and ad-hoc. Overall, the lecture provides a comprehensive understanding of how subtyping influences type systems and polymorphic behavior in programming.