摘要：We begin with an introdution to quiver representations and recall basic notions of Lie algebras. A famous theorem of Gabriel says that a quiver has finite representation type if and only if it is a disjoint union of Dynkin quivers. This surprising connection between quiver representations and Lie theory needs to be explained. In 1990 Ringel constructed an algebra from the module category of a Dynkin quiver, which is isomorphic to the postive part of the quantized envelopping algebra of the corresponding simple Lie algebra. This is the so-called Ringel-Hall algebra. We shall also include a geometrical proof of Gabriel's Theorem in this talk.