Concepts of Symmetry in the Work of Wolfgang Pauli

"Symmetry" was one of the most important methodological themes in 20th-century physics and is probably going to play no lesser role in physics of the 21st century. As used today, there are a variety of interpretations of this term, which differ in meaning as well as their mathematical consequences. Symmetries of crystals, for example, generally express a different kind of invariance than gauge symmetries, though in specific situations the distinctions may become quite subtle. I will review some of the various notions of "symmetry" and highlight some of their uses in specific examples taken from Pauli's scientific oevre.