We present the chemical composition of 206 red giant branch stars that are members of the Small Magellanic Cloud (SMC) using optical high-resolution spectra collected with the multi-object spectrograph FLAMES-GIRAFFE at the ESO Very Large Telescope. This sample includes stars in three fields that are located in different positions within the parent galaxy. We analysed the main groups of elements, namely light- (Na), α- (O, Mg, Si, Ca, and Ti), iron-peak (Sc, V, Fe, Ni, and Cu), and s-process elements (Zr, Ba, and La). The metallicity distribution of the sample displays a main peak around [Fe/H]∼–1 dex and a weak metal-poor tail. However, the three fields display different [Fe/H] distributions. In particular, a difference of 0.2 dex is found between the mean metallicities of the two innermost fields. The fraction of metal-poor stars increases significantly (from ∼1 to ∼20%) from the innermost fields to the outermost field, likely reflecting an age gradient in the SMC. We also found an indication of possible chemically and kinematic distinct substructures. The ratios of the SMC stars are clearly distinct from those of Milky Way stars, in particular, for the elements produced by massive stars (e.g. Na, α, and most iron-peak elements), whose abundance ratios are systematically lower than those measured in our Galaxy. This shows that massive stars contributed less to the chemical enrichment of the SMC than the Milky Way, according to the low star formation rate expected for this galaxy. Finally, we identified small systematic differences in the abundances of some elements (Na, Ti, V, and Zr) in the two innermost fields, suggesting that the chemical enrichment history in the SMC has not been uniform.