‘Symmetry’ comes from the Greek word συμμετρος, meaning well-ordered. Symmetry is present in many fields. Several objects in Nature are geometrically symmetrical, for example a butterfly, or a flower, or a fullerene molecule.

Symmetry is used in physics in several different ways, exploiting its mathematical description. In modern physics, it is used as a powerful instrument to constrain the form of equations. The equations are assumed to be invariant under the transformation of a group, which may be discrete or a continuous Lie group. This approach is of fundamental importance, in particular, for particle physics.

This chapter begins with a simple classification of the various types of symmetry, introducing the concepts that will be ...

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