Abstract: In this series of two talks after defining di(rected )graphs, path algebras and incidence algebras (which are quotients of certain path algebras) we'll focus on LPAs (Leavitt path algebras, a universal localization of path algebras). The interplay between the geometry of the digraph and the algebraic and representation theoretic properties of the LPA will be discussed. Representations of an LPA turn out to be a full subcategory (defined by a natural isomorphism condition) of quiver representations of the relevant digraph. In particular all finite dimensional representations of LPAs are classified (in sharp contrast to quiver representations). I expect to spend most of the time on results from an ongoing research project with Ayten Koc (funded by TUBITAK grant 122F414) on isomorphism and Morita invariants of LPAs of polynomial growth, but earlier joint work with Muge Kanuni on the IBN (invariant basis number) property of LPAs and more recent joint work with Elizabeth Pacheco on irreducible representations of LPAs will also be mentioned. These talks should be accessible to graduate students having some familiarity with modules over rings. All the relevant terms will be defined and there will be many examples.