Molecular hydrogen in absorption at high redshifts

Absorption lines from molecular hydrogen ($\rm H_2$) in the spectra of background sources are a powerful probe physical conditions intervening cold neutral medium. At high redshift, $z>2$, $\rm H_2$ conveniently shifted optical domain, allowing use ground-based telescopes to perform high-resolution spectroscopy, which is essential for proper analysis gas. We describe recent observational progress, based on development efficient pre-selection techniques low-resolution spectroscopic surveys such as Sloan Digital Sky Survey (SDSS). The next generation spectrographs with blue-throughput, CUBES, will certainly significantly boost efficiency and outcome follow-up observations. In this paper, we discuss priority science cases building observations at high-z: probing phase regular galaxies outflowing gas active galactic nucleus.