Differential characters and multiplicative cohomology

This thesis attemps to compare the groups of di¤erential characters of Cheeger Simons to Karoubi?s multiplicative cohomology. Also, we give a description of the group of di¤erential characters which is similar to the one of multiplicative cohomology. This similarity follows from quotients of Karoubi?s modied cochains by di¤erent equivalence relations Keywords : Di¤erential forms,filtration, de Rham cohomology, di¤erential char- acters, multiplicative cohomology.