  Symmetries play a central role in QFT. In order to characterize a special symmetry one has to specify transformations T and features that remain unchanged during these transformations: invariants I. Symmetries are thus pairs \(\{\)T, I\(\}\). The basic idea is that the transformations change elements of the mathematical description (the Lagrangians for instance) whereas the empirical content of the theory is unchanged. There are space-time transformations and so-called internal transformations. Whereas space-time symmetries are universal, i. e., they are valid for all interactions, internal symmetries characterize special sorts of interaction (electromagnetic, weak or strong interaction). Symmetry transformations define properties of particles/quantum fields that are conserved if the symmetry is not broken. The invariance of a system defines a conservation law, e.g., if a system is invariant under translations the linear momentum is conserved, if it is invariant under rotation the angular momentum is conserved. Inner transformations, such as gauge transformations, are connected with more abstract properties.