Topological quantum field theory is an area of mathematical physics that studies topological invariants, which are properties of topological spaces invariant under homeomorphisms. A topological quantum field theory (TQFT) is a collection of manifolds and vector spaces assigned to those manifolds; a homeomorphism between manifolds is assigned an isomorphism between their vector spaces. TQFTs come with four axioms, which we will use to show two elementary results. We define a Frobenius algebra, and show that the two-dimensional TQFTs are in a bijective correspondence with finite dimensional Frobenius algebras.