What territories were conquered by Rome during the Roman Empire and when the Roman state reached its largest size?

Conquered: Gaul, Carthage, Spain (Lusitania), Numidia, Mauritania, Britain except Caledonia), Egypt, Greece, Macedonia, Illyria, Asia Minor, Syria, Palestine, Armenia. Also part of Germany, Arabia, Mesopotamia and Transcaucasia, the southern coast of Crimea.

It is believed that the Roman Empire reached its largest size during the time of Emperor Trajan in the 2nd century AD. Then, temporarily, Roman troops reached the Caspian Sea, the Persian Gulf and subdued the Black Sea coast.