Roman baths in Paris
One of the things the Romans are most famous for is their architecture. The Romans brought a lot of new ideas to architecture, of which the three most important are the arch, the baked brick, and the use of cement and concrete.
Around 700 BC the Etruscans brought West Asian ideas about architecture to Italy, and they taught these ideas to the Romans. We don't have much Etruscan architecture left, but a lot of their underground tombs do survive, and some traces of their temples.
The first Roman emperor, Augustus, made more changes: he built a lot of brick and marble buildings, including a big Altar of Peace and a big tomb for his family, and a big stone theater for plays. Augustus' stepson Tiberius rebuilt the Temple of Castor and Pollux in the Roman forum.
Then in 69 AD Vespasian tore down some of the Golden House to build the Colosseum. Vespasian's son Titus built a great triumphal arch, and his other son Domitian built a great palace for himself on the Palatine hill.
Even though Domitian was assassinated in 96 AD, later architects continued to use the techniques that had been developed for his palace, just as later emperors continued to live in Domitian’s palace. Trajan’s architect used brick and concrete arches to build a new forum with a big column in it and an elaborate market building that is the source of modern shopping malls. Trajan also built the first major public bath building in Rome. It may have been the same architect who later designed Hadrian's Pantheon, a temple to all the gods, which used brick and concrete to build a huge dome. Nobody would build a bigger dome for more than a thousand years.