Quiver representation theory is a fundamental tool in modern representation theory of associative algebras. A cornerstone of this field is Gabriel’s theorem, which characterizes quivers with finitely many indecomposable representations as precisely those arising from Dynkin diagrams of type ADE. This result provided an early glimpse into a profound connection between quiver representations and Lie theory, one that has since led to remarkable developments, including Lusztig’s theory of canonical bases in quantum groups and Nakajima’s quiver varieties in geometric representation theory. In this talk, we will give an accessible introduction to this interplay, starting with the theorems of Gabriel and Kac and culminating in Ringel’s realization of the positive half of quantum groups through Ringel-Hall algebras.