  The central topic of this thesis is the study of some properties of a class
of complex compact manifolds~: Moishezon manifolds. In the first part, we
generalize J.-P. Demailly's holomorphic Morse inequalities to the case of a
line bundle equipped with a metric with analytic singularities on an arbitrary
compact complex manifold. Our inequalities give an estimate of the cohomology
groups with values in the line bundle tensor powers twisted by the
corresponding sequence of multiplier ideal sheaves introduced by Nadel. As a
consequence, we obtain a necessary and sufficient analytic condition, invariant
by bimeromorphism, for a manifold to be Moishezon. In the second part, we use
Mori theory to analyze the structure of Moishezon manifolds with infinite
cyclic Picard group, with big canonical bundle, and which become projective
after one single blow-up with smooth center. We study the dimension and the
structure of the center of the blow-up. In dimension four, we show that this
locus is always a surface, and when the canonical bundle
