This lecture is designed to be understood by a general mathematical audience, including graduate students with some background in basic algebraic concepts (such as would be covered in an introductory graduate course in algebra, plus low-level familiarity with the concept of an affine/projective algebraic variety).

We will start by discussing the ultimate classification goal in the study of a finite dimensional (associative) algebra $A$ over an algebraically closed field, illustrate this goal with some first examples, and introduce the concepts of finite, tame, and wild representation type. In particular, this will lead us to representations of algebras given by quiver and relations, which are located at the heart of this sequence of talks (we will introduce them here, no prior familiarity is required).