  This thesis concerns the research on a Lorentzian generalization of Alain
Connes' noncommutative geometry. In the first chapter, we present an
introduction to noncommutative geometry within the context of unification
theories. The second chapter is dedicated to the basic elements of
noncommutative geometry as the noncommutative integral, the Riemannian distance
function and spectral triples. In the last chapter, we investigate the problem
of the generalization to Lorentzian manifolds. We present a first step of
generalization of the distance function with the use of a global timelike
eikonal condition. Then we set the first axioms of a temporal Lorentzian
spectral triple as a generalization of a pseudo-Riemannian spectral triple
together with a notion of global time in noncommutative geometry.
