  Building on the experience of the high-resolution community with the suite of
VLT high-resolution spectrographs, which has been tremendously successful, we
outline here the (science) case for a high-fidelity, high-resolution
spectrograph with wide wavelength coverage at the E-ELT. Flagship science
drivers include: the study of exo-planetary atmospheres with the prospect of
the detection of signatures of life on rocky planets; the chemical composition
of planetary debris on the surface of white dwarfs; the spectroscopic study of
protoplanetary and proto-stellar disks; the extension of Galactic archaeology
to the Local Group and beyond; spectroscopic studies of the evolution of
galaxies with samples that, unlike now, are no longer restricted to strongly
star forming and/or very massive galaxies; the unraveling of the complex roles
of stellar and AGN feedback; the study of the chemical signatures imprinted by
population III stars on the IGM during the epoch of reionization; the exciting
possibility of paradigm-changing contributions to fundamental physics. The
requirements of these science cases can be met by a stable instrument with a
spectral resolution of R~100,000 and broad, simultaneous spectral coverage
extending from 370nm to 2500nm. Most science cases do not require spatially
resolved information, and can be pursued in seeing-limited mode, although some
of them would benefit by the E-ELT diffraction limited resolution. Some
multiplexing would also be beneficial for some of the science cases. (Abridged)
