This white paper emphasizes the potential of QSO absorption lines in the rest-frame far/extreme UV at rest-frame wavelengths from ~500 to 2000 A. In this wavelength range, species such as Ne VIII, Na IX, and Mg X can be detected, providing diagnostics of gas with temperatures >> 10^{6} K, as well as banks of adjacent ions such as O I, O II, O III, O IV, O V, and O VI (and similarly N I - N V; S II - S VI; Ne II - Ne VIII, etc.), which constrain physical conditions with unprecedented precision. A UV spectrograph with good sensitivity down to observed wavelengths of 1000 A can detect these new probes in absorption systems with redshift z(abs) > 0.3, and at these redshifts, the detailed relationships between the absorbers and nearby galaxies and large-scale environment can be studied from the ground. By observing QSOs at z = 1.0 - 1.5, HST has started to exploit extreme-UV QSO absorption lines, but HST can only reach a small number of these targets. A future, more sensitive UV spectrograph could open up this new discovery space.
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