Projective modules in commutative algebra correspond to vector bundles in algebraic geometry. In 1955, Serre raised the question of whether every vector bundle on affine n-space A^n is trivial, or equivalently, whether every projective module over a polynomial ring k[x_1,...,x_n] is free. The Quillen-Suslin Theorem says that this is true, and we will present a proof due to Vaserstein. Speaker(s): Michael Mueller (University of Michigan)