Abstract : In this thesis we study string theory with D-branes and possibly
orientifolds in curved or time-dependent spaces. Our study aims at
understanding some aspects of curved and time-dependent spaces, notably because of their importance in cosmology.
The first chapter introduces some bases of string theory.
The second chapter studies non-oriented strings on compact groups SU(2) and SO(3): after reviewing known results about D-branes in such spaces, we present our results on the position of orientifolds and their interaction with open and closed strings.
The third chapter studies D-branes in certain backgrounds of Ramond-Ramond type, using S-duality, which links them with backgrounds of Neveu-Schwarz type, where calculations can be done.
The last chapter considers strings on a D-brane embedded with a plane wave, and introduces tools which allow to study interactions in such a background.