This is the first lecture of the course financed by INDAM on "quiver representations". This course is an introduction to quivers and their representations, with a focus on applications to the representation theory of finite dimensional algebras. Topics covered in the course include: representations of quivers, direct sums, morphisms, kernels, exact sequences, projective and injective representations, Auslander-Reiten quiver, algebras, modules, idempotents, path algebras, Auslander-Reiten theory. We will use the language of category theory throughout the course.