• cell complexes
• hyperbolic manifolds
• hyperbolization procedures

The main subject of the thesis is to investigate on hyperbolization procedures for cell complexes, i.e. on particular functors from some category of cell complexes, to the category of metrized cell complexes. Such a procedure is interesting because it produces complete geodesic metric spaces with bounded curvature, and, in some cases, word hyperbolic groups in the sense of Gromov.
In the first chapter we introduce some basic definitions concerning metric spaces and spaces of curvature bounded from above. In the second chapter we deal with cell complexes, in particular metrized cell complexes. We explain some criteria in order to understand whenever such spaces admit a non-positive or strictly negative curvature. The objects of the third chapter are Coxeter Groups and Coxeter orbifolds, used in the fourth chapter in order to prove weaknesses of some old hyperbolization procedures. In the last two chapters, following the work of Charney and Davis, we present a strict hyperbolization procedure which yelds piecewise hyperbolic cell complexes with strictly negative curvature. This construction concerns particular "manifolds with corners", generated from closed hyperbolic manifolds in arbitrary dimension which involve the arithmetic of quadratic forms.