Jena lectures on generalized global symmetries: principles and applications

This is an elementary set of lectures on generalized global symmetries originally given at the Jena TPI School on QFT and Holography, designed to be accessible to the reader with a basic knowledge of quantum field theory. Topics covered include an introduction to higher-form symmetries with selected applications: Abelian and non-Abelian gauge theories in the continuum and on the lattice, statistical mechanical systems, the Adler-Bell-Jackiw anomaly from the point of view of non-invertible symmetry, and magnetohydrodynamics. Mathematical formalism is kept to a minimum and an emphasis is placed on understanding the global symmetry structure present in well-known models.