Notes on Factorization Algebras and TQFTs

These are notes from talks given at a spring school on topological quantum field theory in Nova Scotia during May of 2023. The aim is to introduce the reader to the role of factorization algebras and related concepts in field theory. In particular, we discuss the relationship between factorization algebras, ${\mathbb{E}}_n$-algebras, vertex algebras, and the functorial perspective on field theories.