 It turned out that requiring invariance under local gauge transformations supplies a systematic way for finding the equations describing fundamental interactions. For instance, starting with the Lagrangian for a free electron, the requirement of local gauge invariance can only be fulfilled by introducing additional terms, namely those for the electromagnetic field. Gauge invariance can be captured by certain symmetry groups: \(\mathrm{U}(1)\) for electromagnetic, \(\mathrm{SU}(2)\otimes\mathrm{U}(1)\) for electroweak and \(\mathrm{SU}(3)\) for strong interaction. This has become an important basis for unification programs, as is the analogy to general relativity where a local gauge symmetry (general covariance) leads to the Einstein-Hilbert theory of the gravitational field. Moreover, gauge invariant quantum field theories are generically renormalizable. (There are many renormalizable theories, but finding theories with massive vector fields was stopped for decades before gauge theories and the Higgs mechanism came into the fore.) All this can be taken to show that a mathematically rich framework, with surplus structures, can be very valuable in the construction of theories.