@article {2010, title = {Gauge theory: from physics to geometry}, journal = {Rend. Istit. Mat. Univ. Trieste 42 (2010) 103-128}, number = {SISSA;80/2010/FM}, year = {2010}, publisher = {Istituto di matematica. Universita\\\' di Trieste}, abstract = {Maxwell theory may be regarded as a prototype of gauge theory and generalized to nonabelian gauge theory. We briey sketch the history of the gauge theories, from Maxwell to Yang-Mills theory, and the identification of gauge fields with connections on fibre bundles. We introduce the notion of instanton and consider the moduli spaces of such objects. Finally, we discuss some modern techniques for studying the topology of these moduli spaces.}, url = {http://hdl.handle.net/1963/4105}, author = {Ugo Bruzzo} }