Basic notions of finite-dimensional algebras

The representation theory of many things, if the "thing" that's being represented is finite in some sense, turns out to be equivalent to studying modules over a finite-dimensional algebra. And a lot of the notions in representation theory can be introduced in this generality. I will mention several of these and their properties in this talk such as: the notion of semisimplicity and the Artin/Wedderburn theorem, radical, socle, the radical/socle series and the Loewy length, indecomposable modules and the Krull-Schmidt theorem, indecomposable projectives/injectives.