This book is the first ever monograph on the topic of Connexive logics, a family of non-classical logics, based on the intuition that a proposition cannot validly imply, nor be implied, by its own negation. Similar to Relevance logics, Connexive logics require a meaning connection between the antecedent and the consequent of a valid implication. The interaction between negation and conditionals, as well as with other connectives, is closer to certain uses of them in natural languages. The book is not a fully comprehensive study of Connexive logics; rather, it presents the author's own view of those logics, with emphasis on the facets of those logics that interest the author. Still, it contains enough material to familiarize the reader with those logics, understand how they originate and how they are motivated, and the proof-theoretic and model-theoretic principles underlying them. It is hoped that this book will contribute to the popularization of Connexive logics and to the growth of the, currently small, community interested in them. Nissim Francez is an emeritus professor of computer science at the Technion, Israel Institute of Technology. At a certain point in his career he moved from research related to concurrent and distributed programming and program verification to research in computational linguistics, mainly formal semantics of natural language. In recent years, he has worked on Proof-Theoretic Semantics, in particular for natural language. More recently, he has worked also on non-classical logics, including Connexive logics.