In modern physics, symmetries are a powerful tool to constrain the form of equations, namely the Lagrangian that describes the system. Equations are assumed to be invariant under the transformation of a given group, which may be discrete or a continuous Lie group. Classification of the various types of symmetry. The concept of spontaneous symmetry breaking. It will evolve into the Higgs mechanism, which gives origin to the masses of the vector bosons that mediate the weak interactions, of the quarks and of the charged leptons.

The discrete symmetries, in particular the parity and the particle–antiparticle conjugation operations and the corresponding quantum numbers.

An important dynamical symmetry of the hadrons, the invariance of the Lagrangian under rigid rotations in an ‘internal’ space, the isospin space. The unitary group is SU(2).

This chapter is divided into two parts. The first part introduces the quark model, following more or less the historical developments. It led to an approximate symmetry, based on the SU(3) flavour group, where u, d and s quarks are the three degrees of freedom. The second part introduces the quantum chromodynamics theory (QCD), i.e. the true formal gauge theory of the strong interaction. Here again, the symmetry group is SU(3), but the degrees of freedom are the three quark colours. This symmetry is assumed to be exact, which has consequences on the existence of gluons and their properties, the carriers of the strong interaction at the elementary particle level, briefly mentioned in the previous chapter. The QCD interaction is the first non-Abelian interaction encountered in the book. The non-perturbative regime of QCD is also presented with a short introduction to lattice QCD. A discussion about the colour confinement and the hadronisation of quarks is also given.