what is this empire?
It was the post-Republican period of ancient Rome.
Roman Empire
The Roman Empire ( ; ) was the post-Republican period of ancient Rome. 
the roman empire reached its greatest extent during the During the reign of Trajan
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Roman Empire [SEP] Introduction
The Roman Empire ( ; ) was the post-Republican period of ancient Rome. As a polity it included large territorial holdings around the Mediterranean Sea in Europe, Northern Africa, and Western Asia ruled by emperors. From the accession of Caesar Augustus to the military anarchy of the third century, it was a principate with Italy as metropole of the provinces and the city of Rome as sole capital (27 BC – 286 AD). After the military crisis, the empire was ruled by multiple emperors who shared rule over the Western Roman Empire (based in Milan and later in Ravenna) and over the Eastern Roman Empire (also known as the Byzantine Empire; centred on Nicomedia and Antioch, later based in Constantinople).