  Endomorphisms algebras can replace the concept of principal fiber bundle.
Gauge theories are reformulated within this algebraic framework and further
generalized to unify ordinary connections and Higgs fields. A 'noncommutative
Maxwell' model is built starting from non trivial fiber bundles thus requiring
the development of the notion of Riemannian structure. The tools involved in
the study of associative algebras are presented and an algebraic method to
characterize the usual Chern-Weil morphism is proposed. Then, current results
on symmetric fiber bundles are generalized to noncommutative connections and an
extension of the Witten ansatz is given. Finally, a generalization of the
Born-Infeld action for noncommutative connections is proposed. The
corresponding Lagrangians are non-polynomial and the existence of solitonic
solutions is shown on several examples
