A quiver is a directed graph, that is, a collection of points and arrows pointing from some points to others. A representation of the quiver is a way of assigning a vector space to each point and a linear transformation to each arrow. We discuss what it means for two representations to be isomorphic. We then show how the theory of representations of quivers captures many of the basic ideas of linear algebra such as similarity and equivalence of matrices. If time permits, we will discuss Gabriel's theorem, one of the most fundamental results in the subject, which classifies those quivers of finite representation type.