An Introduction to Frobenius Algebras and 2D TQFTs

This thesis explores the equivalence between two dimensional topological quantum field theories and Frobenius algebras. We first provide a complete presentation by generators and relations of the $2$-dimensional oriented bordism category as a symmetric monoidal category. This presentation is then used to classify the $2$-dimensional topological field theories with values in an arbitrary target symmetric monoidal category.