Results obtained from an X-ray spectral survey of nearby Seyfert galaxies using XMM--Newton are reported. The sample was optically selected, well defined, complete in B mag, and distance limited: it consists of the nearest (D<22 Mpc) 27 Seyfert galaxies (9 of type 1, 18 of type 2) taken from the Ho et al. (1997) sample. This is one of the largest atlases of hard X-ray spectra of low-L active galaxies ever assembled. All nuclear sources except two Sey 2s are detected between 2-10 keV, half for the first time ever, and average spectra are obtained for all of them. Nuclear luminosities reach values down to 10**38 erg/s. The shape of the distribution of X-ray parameters is affected by the presence of Compton-thick objects (> 30% among type 2s). The latter have been identified either directly from their intense FeK line and flat X-ray spectra, or indirectly with flux diagnostic diagrams which use isotropic indicators. After taking into account these highly absorbed sources, we find that (i) the intrinsic X-ray spectral properties (i.e., spectral shapes and luminosities above 2 keV) are consistent between type 1 and type 2 Sey, as expected from ``unified models, (ii) Sey galaxies as a whole are distributed fairly continuously over the entire range of Nh, between 10**20 and 10**25 cm**-2, and (iii) while Sey 1s tend to have lower Nh and Sey 2s tend to have the highest, we find 30% and 10% exceptions, respectively. Overall the sample well represents the average intrinsic X-ray spectral properties of nearby AGN, including a proper estimate of the distribution of their absorbing columns. Finally, we conclude that, with the exception of a few cases, the present study agrees with predictions of unified models of Sey galaxies, and extends their validity down to very low luminosities.