  This paper presents relevant modern mathematical formulations for (classical)
gauge field theories, namely, ordinary differential geometry, noncommutative
geometry, and transitive Lie algebroids. They provide rigorous frameworks to
describe Yang-Mills-Higgs theories or gravitation theories, and each of them
improves the paradigm of gauge field theories. A brief comparison between them
is carried out, essentially due to the various notions of connection. However
they reveal a compelling common mathematical pattern on which the paper
concludes.
