  Very high energy physics needs a coherent description of the four fundamental
forces. Non-commutative geometry is a promising mathematical framework which
already allowed to unify the general relativity and the standard model, at the
classical level, thanks to the spectral action principle. Quantum field
theories on non-commutative spaces is a first step towards the quantification
of such a model. These theories can't be obtained simply by writing usual field
theory on non-commutative spaces. Such attempts exhibit indeed a new type of
divergencies, called ultraviolet/infrared mixing, which prevents
renormalisability. H. Grosse and R. Wulkenhaar showed, with an example, that a
modification of the propagator may restore renormalisability. This thesis aims
at studying the generalization of such a method. We studied two different
models which allowed to specify certain aspects of non-commutative field
theory. In x space, the major technical difficulty is due to oscillations in
the interaction part. We generalized the results of T. Filk in order to exploit
such oscillations at best. We were then able to distinguish between two
mixings, renormalizable or not. We also bring the notion of orientability to
light : the orientable non-commutative Gross-Neveu model is renormalizable
without any modification of its propagator. The adaptation of multi-scale
analysis to the matrix basis emphasized the importance of dual graphs and
represents a first step towards a formulation of field theory independent of
the underlying space.
