Clavius Base is a Lunar Research base. It was one of the largest permanent lunar bases. The vast majority of the structures were underground, but some were built above ground.
When the Tycho Monolith was discovered in 2001, all outside contact with Clavius was shut down. Whenever someone tried to contact the base, all one could get was a recording that said the phone lines were "temporarily out of order". A cover story was placed that an epidemic had broken out at the Base.
Dr. Heywood Floyd took a very secretive government trip to Clavius to investigate TMA-1. After his arrival, a short briefing was given before he was shuttled to Tycho.