We present a forthcoming library of M dwarf spectra taken with the ultra-high resolution spectrograph PEPSI (R = 250 000). Our library consists of 7 nearby inactive M dwarfs spanning spectral types M0 to M7, including known planet hosts GJ581 (M3), Barnard’s Star (M4), and Teegarden’s Star (M7). The wavelength coverage (383 — 906 nm) approximately captures the peak of the M dwarf flux density distribution. In particular, the 700 — 900 nm window is information-rich and suitable for chemical abundance measurements. We show examples of exquisitely resolved atomic and molecular features and compare them with models. While some features, like the hyperfine structure of vanadium, are remarkably well-described by synthetic spectra, others show severe mismatches with state-of-the-art models, highlighting their limitations. The PEPSI spectral templates will be an invaluable resource for the community by enabling precise radial velocity measurements, as well as detailed tests of cool dwarf atmosphere models and refinements of relevant line lists for chemical analysis.