  These notes offer a lightening introduction to topological quantum field
theory in its functorial axiomatisation, assuming no or little prior exposure.
We lay some emphasis on the connection between the path integral motivation and
the definition in terms symmetric monoidal categories, and we highlight the
algebraic formulation emerging from a formal generators-and-relations
description. This allows one to understand (oriented, closed) 1- and
2-dimensional TQFTs in terms of a finite amount of algebraic data, while
already the 3-dimensional case needs an infinite amount of data. We evade these
complications by instead discussing some aspects of 3-dimensional extended
TQFTs, and their relation to braided monoidal categories.
