Spontaneous broken symmetry

The concept of spontaneous broken symmetry is reviewed in the presence of global symmetries both in matter and particle physics. This concept is then taken over to confront local symmetries in relativistic field theory. Emphasis is placed on the basic concepts where, in the former case, the vacuum of spontaneous broken symmetry is degenerate whereas that of local (or gauge) symmetry is gauge invariant. To cite this article: R. Brout, F. Englert, C. R. Physique 8 (2007).