TY - JOUR T1 - Gauge theory: from physics to geometry JF - Rend. Istit. Mat. Univ. Trieste 42 (2010) 103-128 Y1 - 2010 A1 - Ugo Bruzzo AB - 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. PB - Istituto di matematica. Universita\\\' di Trieste UR - http://hdl.handle.net/1963/4105 U1 - 299 U2 - Mathematics U3 - Mathematical Physics ER -