We present a complete library of synthetic spectra based on Kurucz ’ s codes that covers the 2500–10 500 Å wavelength range at resolving powers R _ { P } =20 000 , 11 500 ( \equiv GAIA ) , 8500 ( \equiv RAVE ) , 2000 ( \equiv SLOAN ) and uniform dispersions of 1 and 10 Å/pix . The library maps the whole HR diagram , exploring 51 288 combinations of atmospheric parameters spanning the ranges : 3500 \leq T _ { eff } \leq 47 500 K , 0.0 \leq \log g \leq 5.0 , - 2.5 \leq [ M/H ] \leq 0.5 , [ \alpha /Fe ] = 0.0 , +0.4 , \xi =1,2,4 km sec ^ { -1 } , 0 \leq V _ { rot } \leq 500 km sec ^ { -1 } . The spectra are available both as absolute fluxes as well as continuum normalized . Foreseen applications of the library are briefly discussed , including automatic classification of data from spectroscopic surveys ( like RAVE , SLOAN , GAIA ) and calibration of differential photometric indexes . Data distribution and access to the library via dedicated web page are outlined .