In the first lectures of the course we have given a very brief introduction about the topic of this course: topological defects in quantum field theories (QFTs).

A short synopsis of the topics covered is as follows:

Mathematics and QFT: Quantum Mechanics (QM) is math, Topological Quantum Field Theory (TQFT) is math, but QFT is not (yet) math (no universally accepted axiom system).
This course is not a course about QFT: rather it is a course about the mathematical structures of topological defects of QFTs, which generalize the notion of symmetries in QFT.
Introductory level discussion about QFTs (continuous fields as sections of bundles, correlation functions, path integrals, Wick rotation, Euclidean fields, RG flow and c-theorems, duality)... we will encounter manifestations of these notions in the context of lattice models
Topological defects and symmetries, the (naive) symmetry category (a higher (d-1)-category enriched in higher (d-2)-category)
Symmetries in Quantum Mechanics
(Naive) symmetries in 2d quantum fields: topological defect lines

Sangiovanni's notes: lecture 2

References:

For some further insights see my lectures at LACES 2024