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Relevant logics are forms of non-classical logic that require the antecedent and consequent of implications to be relevantly related. They are paraconsistent logics, i.e. they are able to robustly handle contradictory information. The field of non-classical logics is rapidly expanding, particularly with the addition of modalities and quantifiers. This is the first book to develop systematically a basic frame theory of relevant logics that includes both modal and quantified extensions. It includes sections comparing features of relevant logics with other, more common logics used in philosophy, examples and exercises to make the material more accessible, and an extensive bibliography. It also includes philosophical discussion of many aspects of relevant logics, and highlights several directions for future research, both philosophical and formal.