  These notes offer an introduction to the functorial and algebraic description
of 2-dimensional topological quantum field theories `with defects', assuming
only superficial familiarity with closed TQFTs in terms of commutative
Frobenius algebras. The generalisation of this relation is a construction of
pivotal 2-categories from defect TQFTs. We review this construction in detail,
flanked by a range of examples. Furthermore we explain how open/closed TQFTs
are equivalent to Calabi-Yau categories and the Cardy condition, and how to
extract such data from pivotal 2-categories.
