This thesis is anchored in the research of better understanding of the chemical evolution of galaxies. Many dwarf spheroidal galaxies (dSph) are orbiting the Milky Way displaying various star formation histories. The formation of these dwarf galaxies and the drivers of their evolution are still not well understood. We studied in detail one of them, Sextans, a low mass dSph composed of an old population. 90% of Sextans stars were formed 11-14 Gyr ago (Lee et al. 2009). Battaglia et al. (2011) show the presence of a radial metallicity gradient in Sextans considering observation based on intermediate resolution spectroscopy until the tidal radius. For a projected radius R < 0.8 deg stars cover the whole range of [Fe/H], while for R > 0.8 deg all stars are metal-poor [Fe/H] < -2.2 dex. Due to its distance and its low surface brightness high resolution spectra are required to obtain accurate abundances. Up to recently only 14 Sextans stars have been observed in high resolution spectroscopy (Shetrone et al. 2001; Aoki et al. 2009; Tafelmeyer et al. 2010; Honda et al. 2011) but in majority they were focused only on extremely metal-poor stars. In order to understand the chemical evolution of Sextans we needed to study a statistically significant sample of stars covering a larger metallicity range. This has been done in this work based on the largest high resolution spectroscopic sample of 87 red giant branch stars ever obtained in such low mass dwarf spheroidal galaxies. Our sample of stars located in the center of Sextans displays a large metallicity distribution ranging from -1.0 dex to -3.5 dex. We derived abundances of 10 elements : 3 alpha-elements (Mg, Ca and Ti), 5 iron-peak elements (Sc, Cr,Mn, Co and Ni) and 2 neutron-capture elements (Ba and Eu). Combining the results we had the first picture of the chemical evolution of Sextans. From [alpha/Fe] distribution reflecting the ratio between supernovae [SNe II/SNe Ia], we found that the domination of SNeIa in chemical evolution occurred around [Fe/H] = -2.0 dex. A lower knee than for Fornax and Sculptor suggests that star formation was less efficient in Sextans in agreement with their respective estimated mass. The absence of intrinsic scatter in [alpha/Fe] showed that in the center of Sextans the interstellar medium has been homogeneously enriched through star formation. Some hypothesis like tidal interactions with the Milky Way could explain this abundance homogeneity in the center of the galaxy and the metallicity gradient toward the outskirts. Abundances in iron-peak elements and neutron-capture elements give new observational constraints for a better understanding of the various nucleosynthesis sources of these elements.