This book is a course in Stone-Priestley duality theory, with applications to logic and theoretical computer science. Our target audience are graduate students and researchers in mathematics and computer science. Our aim is to get in a fairly full palette of duality tools as directly and quickly as possible, then to illustrate and further elaborate these tools within the setting of three emblematic applications: semantics of propositional logics, domain theory in logical form, and the theory of

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... profinite monoids for the study of regular languages and automata. This preprint version contains the first part of the book, a graduate level 'crash course' in duality theory as it is practiced now, and a chapter on applications to domain theory.