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Studying logics via semantics is a well-established and very active branch of mathematical logic, with many applications, in computer science, philosophy, and elsewhere. The area is characterized by results, tools and techniques stemming from various fields, including universal algebra, topology, category theory, order, and model theory. The programme of the conference TACL 2024 will focus on three interconnecting mathematical themes central to the semantic study of logics and their applications: algebraic, categorical, and topological methods.