2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/3303Damped Lyman alpha systems seen in the spectra of high-z QSOs arise in high-density neutral gas in which molecular hydrogen (H_2) should be conspicuous. Systematic searches to detect the H_2 lines redshifted into the Lyman alpha forest at <3400Åare now possible thanks to the unique capabilities of UVES on the VLT. Here we summarise the present status of our on going programme to search for H_2 in DLAs, discuss the physical conditions in the systems where H_2 is detected and the implications of non-detections.4 pages. To appear in the Proceedings of the XVII IAP Colloquium "Gaseous Matter in Galaxies and Intergalactic Space"Astrophysicstext