Which Italian architect inspired by classical Greece and Rome designed and complete the dome shown here?

The Italian architect you are referring to is Michelangelo Buonarroti, who designed the dome of St. Peter's Basilica in Vatican City. Inspired by classical Greek and Roman architecture, Michelangelo's design features a harmonious blend of proportions and a grand scale, reflecting the Renaissance ideals of beauty and symmetry. The dome was completed after his death in 1590, with the final construction elements carried out by other architects.