Starting from classical problems in linear algebra and experiencing a spectacular development in the last forty years, the theory of representations of finite dimensional algebras is today one of the most popular and active fields in algebra. New theoretical approaches (like the use of quiver-theoretical techniques, the introduction of almost split sequences and Auslander-Reiten theory, the development of tilting theory, the notion of Gabriel-Roiter measure, the theory of Ringel-Hall algebras, the results in cluster theory) and the development of new computational algebra packages and [...]
