One of the purposes of stellar spectral classification is to identify stars suitable for synthesising stellar populations. One of the limitations in the classification of stellar spectra is the lack of good training data at high resolution. With this and also the application of population synthesis in mind, I present a high resolution library of 6410 synthetic stellar spectra which I have generated from the Kurucz model and atmospheres. The library covers the wavelength range 3000 - 10 000 Å with 54 values of effective temperature in the range 5250 - 50 000 K, 11 values of log surface gravity between 0.0 and 5.0 and 19 metallicities in the range - 5.0 to 1.0. By comparing the new synthetic spectra with a library of observed spectra, STELIB (Le Borgne et al., 2003), I demonstrate their suitability for the application of population synthesis. I then extend this library by supplementing the Kurucz spectra with other synthetic spectra, to form a library for population synthesis that is similar to that of Lejeune et al. (1998) but at higher resolution (2 Å). As an initial demonstration of the usefulness of this library, I generate some Simple Stellar Population models using PEGASE and study the variation in Lick indices with age and metallicity of the populations. I also investigate two methods of empirical population synthesis however I find that even with modern computational resources these methods are not suitable for the number and size of current spectra.