We present an optical spectral atlas of stars covering the whole M-dwarf sequence. It consists of 95 M dwarfs at solar metallicity observed at low-resolution with EMMI@NTT and 21 M-subdwarfs, extreme-subdwarfs and ultra-subdwarfs observed at high resolution with UVES@VLT. Using the most recent PHOENIX BT-Settl stellar model atmospheres we perform a detailed comparison with our observed spectra using χ^2 minimization technique. We confront the models with low-resolution spectra of M dwarfs at solar metallicity and we assign effective temperatures to the M dwarfs. We present temperature versus spectral type and colour relations and their comparison with others found in the literature. We also present our high-resolution spectra of the subdwarfs (sdM, esdM, usdM) and compare them to the newest grid of the BT Settl models which uses the revised solar abundances of Caffau et al (2011). This comparison allows us to study the spectral details of cool atmospheres, to determine precise [Fe/H] values for our objects, and to investigate the effect of metallicity on cool dwarf atmospheres. This study also helps to validate the atmosphere models and improve them by determining new constants on molecular opacities, dust cloud formation etc.