Galaxy evolution is well constrained up to the first billion years of the Universe. Beyond this limit and considering the few number of sources with z >6.0 confirmed, it appears difficult to constrain the role played by the first galaxies during this period. One of the main goal of this thesis was to study the evolution of the luminosity function for star forming galaxies during the first billion years by using a representative sample of high-redshift objects (z >4.5) bright enough to be observed by spectroscopy. Thus, we have analyzed two different fields of view: one behind the lensing cluster A2667 and another one behind a large blank field (the WUDS survey). The analysis of the A2667 field showed a contamination rate of our sample of about 80%. We combined our observations with far IR data. Using these new data, we highlighted the existence of an extreme type of galaxies strongly affected by dust, which can only be removed from high-z samples by adding data in the far infra-red domain. Using spectroscopic follow up, we have detected another kind of contaminant at low-z combining two different stellar populations with different ages, and which cannot be removed from our sample excepted by using very deep images in the optical bands beyond the limits of current observations. From our samples we were able to add strong constraints on the bright-end of the luminosity function, and then we deduced its evolution during the first billion years of the Universe. Evolution of the LF allows us to deduce the UV density produced by these galaxies during the cosmic reionization, and to show that the relatively bright galaxies currently detected can not be the sole contributors.