Abstract : This work has been devoted to the theoretical study of bulk semimetallic bismuth with methods based on the density functional theory (DFT). Effects of spin-orbit coupling and of the exchange-and-correlation functionals in the local density (LDA) and generalized gradient approximation (GGA) have been systematically investigated. I have found that electron and hole pockets at the Fermi level are accurately reproduced, which has enabled me to successfully interpret the pump-probe experiments in the photoexcited bismuth performed in the Laboratoire des Solides Irradiés. The strong dependence on the electronic wave vector, of the calculated electronic coupling of the upper valence band with the zone-center A1g LO phonon, explains the observation of a strongly k-dependent oscillation amplitude of the upper valence band in time-resolved photoemission experiments upon activation of the coherent A1g phonon under photoexcitation. I have also shown that the presence of local extrema in the conduction and valence bands structure, where the carrier mass can be as large as 18 m0, favours an accumulation of photoexcited carriers in these extrema and contributes to the augmentation of the plasma frequency as a function of time after the photoexcitation, an effect which has no analogy in other materials (as yet). Finally, I have developed a new ab initio approach in the time-dependent density functional perturbation theory (TDDFPT), which allows us to calculate the electronic response of materials for any momentum transfer. This approach based on the Lanczos recursion method has enabled me to calculate for the first time the electron energy-loss spectrum of Bi in the 0-100 eV energy range, bridging the gap between valence and core losses. This method opens the way to the routine calculation of surface plasmons.