In the last decade, the concept of symmetry in quantum field theory has been vastly generalized, to so-called higher-form symmetries, and, more broadly, categorical symmetries, which can sometimes be non-invertible. If these statements sound weird to you, this lecture series is aimed at you.

I will introduce these generalized symmetries using the viewpoint of gauge (Maxwell and Yang-Mills) theories and anomalies, which both motivate the introduction of the new concepts and illustrate them.

Topics covered:

• Charge conservation and global symmetries in Maxwell theory
• Anomalies and higher-group symmetries
• Self-dual Yang-Mills theories and non-invertible symmetries
• Higher categories as the framework for describing symmetries