Electron hole pair condensation at the semimetal semiconductor transition Metall Isolator Phasenumwandlung Bose Einstein Kondensation Ladungsdichtewelle metal insulator transition Bose Einstein condensation charge density wave In this thesis we have revisited the formation of the excitonic insulator (EI) which realizes an exciton condensate. In contrast to optically created exciton condensates the EI forms in thermal equilibrium and is solely driven by the Coulomb attraction between electrons and holes. The EI phase is anticipated to occur near the semimetal semiconductor (SM SC) transition at low temperatures. Depending from which side the EI is approached it forms due to a BCS type condensation of electron hole pairs or a Bose Einstein condensation (BEC) of excitons. The extended Falicov Kimball model (EFKM) is the minimal model the EI can be described with. This model describes spinless fermions in two dispersive bands (f band and c band) that interact via a local Coulomb repulsion. The EFKM is also used to describe electronic ferroelectricity (EFE). Both phases the EI and EFE type ordering are characterized by a spontaneous f c hybridization in the EFKM. We have presented the EI phase the EFE phase and the orderings they compete with. Moreover we have determined the ground state phase diagram of the EFKM. We have focused particularly on the anticipated BCS BEC crossover within the EI and have analyzed the formation scenarios. The exciton spectrum and the exciton density in the normal phase close to the critical temperature give information about relevant particles and therefore the nature of the transition. We have demonstrated that the whole EI is surrounded by a halo that is a ...