  (abridged) The far-UV wavelength range (912-2000A) provides access to atomic
and molecular transitions of many species the interstellar medium (ISM),
circumgalactic medium (CGM), and intergalactic medium, within phases spanning a
wide range of ionization, density, temperature, and molecular gas fraction.
Far-UV space telescopes have enabled detailed studies of the ISM in the Milky
Way thanks to absorption features appearing in the UV spectra of hot stars and
yielding fundamental insights into the composition and physical characteristics
of all phases of the ISM along with the processes that influence them. However,
we have yet to design a spectrometer able to observe the full UV domain at
resolving power R>10^5 with a signal-to-noise ratio SNR>500. Such a resolution
is necessary to resolve lines from both the cold molecular hydrogen and the
warm metal ions with a turbulent velocity of about 1 km s-1, and to
differentiate distinct velocity components. Future UV spectroscopic studies of
the Milky Way ISM must revolutionize our understanding of the ISM as a
dynamical, unstable, and magnetized medium, and rise to the challenge brought
forward by current theories. Another interesting prospect is to transpose the
same level of details that has been reached for the Milky Way to the ISM in
external galaxies, in particular in metal-poor galaxies, where the ISM chemical
composition, physical conditions, and topology change dramatically, with
significant consequences on the star-formation properties. Finally, we need to
be able to perform statistical analyses of background quasar lines of sight
intersecting the CGM of galaxies at various redshifts and to comprehend the
role of gas exchanges and flows for galaxy evolution.
