This Ph.D. thesis is devoted to the study of the geometry of curved Yang-Mills-Higgs gauge theory (CYMH GT), a theory introduced by Alexei Kotov and Thomas Strobl. This theory reformulates classical gauge theory, in particular, the Lie algebra is generalized to a Lie algebroid E, equipped with a connection ∇, and the field strength has an extra term ζ. The shortened main results of this Ph.D.thesis are the following: 1. A thorough introduction and a coordinate-free formulation of CYMH GT. The infinitesimal gauge transformation will be generalized to a derivation on vector bundle V-valued functionals, induced by a Lie algebroid connection. 2.We take the connection on W then in such a way that the commutator is again an infinitesimal gauge transformation. 3. Defining an equivalence relation of CYMH GTs preserving the physics. We study whether there are equivalence classes admitting representatives with flat ∇ and/or zero ζ.