The Galileo (NCC-1701-7) was a Federation Class F shuttlecraft that was in service with Starfleet in the mid-23rd century, attached to the USS Enterprise. Here is infographic exploring the design and background of the famous shuttlecraft. This also shows the beginning of the restoration progress.

Find out all about Star Trek's Galileo shuttlecraft in this SPACE.com infographic.
Source SPACE.com: All about our solar system, outer space and exploration