This is an overview of the main developments in formal logic throughout Greek antiquity. Topics to be covered include: Aristotle's theory of the categorical syllogism and its application in demonstrative science, Theophrastus' theory of the hypothetical syllogism, Stoic propositional logic, the development of modal logic from Aristotle to the Stoics, Galen's account of relational syllogisms, and the reception of Peripatetic and Stoic logic in late antiquity. Secondary readings will be drawn from Jonathan Barnes, Susanne Bobzien, and Michael Frede, among others.