What is Abstract Algebraic Logic?

Our aim is to answer the question of the title, explaining which kind of problems form the nucleus of the branch of algebraic logic that has come to be known as Abstract Algebraic Logic. We give a concise account of the birth and evolution of the field, that led from the discovery of the connections between certain logical systems and certain algebraic structures to a general theory of algebraization of logics. We consider first the so-called algebraizable logics, which may be regarded as a paradigmatic case in Abstract Algebraic Logic; then we shift our attention to some wider classes of logics and to the more general framework in which they are studied. Finally, we review some other topics in Abstract Algebraic Logic that, though equally interesting and promising for future research, could not be treated here in detail.