This course is an introduction to representation theory of algebras, with an emphasis on group algebras, path algebras of quivers, and their representations. Topics we will cover include composition series, the Jordan—Hölder Theorem, semisimple algebras, Jacobson radicals, the Artin—Wedderburn Theorem, Maschke's Theorem, and the Krull—Schmidt Theorem. We will also learn about representation types of algebras, representations of quivers, and Gabriel's Theorem.