The Enterprise is a Federation ship (NCC-1701). Captain Kirk leads the crew. Galileo shuttlecraft are assigned on board the ship. The space questers on board the Enterprise have been known to eat at Monolith Burger. Cliffy once got into scuffle with the crew of the Enterprise, after he told them they were getting a little old for running around the universe. They are known for not only traveling through space but also time.
At a later time, Captain Picard took over the ship, or rather one of its later models (1701-D). This ship used the later 1701-D shuttlecraft.