This is what’s left of the roof of one of the buildings in the Villa Adriana, also in Tivoli. The Villa Adriana is a Roman palace that was built by emperor Hadrian. When the Villa d’Este was built by cardinal Ippolito II d’Este, he used the Villa Adriana as a source of inspiration (and a source of marble, too).
This is photo 9 of 13 from the Italy series.