  Nowadays, noncommutative geometry is a growing domain of mathematics, which
can appear as a promising framework for modern physics. Quantum field theories
on "noncommutative spaces" are indeed much investigated, and suffer from a new
type of divergence called the ultraviolet-infrared mixing. However, this
problem has recently been solved by H. Grosse and R. Wulkenhaar by adding to
the action of a noncommutative scalar model a harmonic term, which renders it
renormalizable.
  One aim of this thesis is the extension of this procedure to gauge theories
on the Moyal space. Indeed, we have introduced a new noncommutative gauge
theory, strongly related to the Grosse-Wulkenhaar model, and candidate to
renormalizability. We have then studied the most important properties of this
action, and in particular its vacuum configurations. Finally, we give a
mathematical interpretation of this new action in terms of a derivation-based
differential calculus associated to a superalgebra.
  This work contains among the results of this PhD, an introduction to
noncommutative geometry, an introduction to epsilon-graded algebras, and an
introduction to renormalization of scalar (wilsonian and BPHZ point of view)
and gauge quantum field theories.
