Trajan ( TRAY-jən; Latin: Caesar Nerva Trajanus; 18 September 53 – August 117) was Roman emperor from 98 to 117. Officially declared optimus princeps ("best ruler") by the senate, Trajan is remembered as a successful soldier-emperor who presided over one of the greatest military expansions in Roman history and led the empire to attain its greatest territorial extent by the time of his death. He is also known for his philanthropic rule, overseeing extensive public building programs and implementing social welfare policies, which earned him his enduring reputation as the second of the Five Good Emperors who presided over an era of peace within the Empire and prosperity in the Mediterranean world.

Trajan was born in Italica, close to modern Seville in present-day Spain, a small Roman municipium founded by Italic settlers in the province of Hispania Baetica. His branch of the gens Ulpia, the Ulpi Traiani, came from the town of Tuder in the Umbria region of Italia. His father Marcus Ulpius Traianus, also born at Italica in Hispania, was a senator, and therefore Trajan was born into a senatorial family.

Trajan rose to prominence during the reign of emperor Domitian. Serving as a legatus legionis in Hispania Tarraconensis, in 89 Trajan supported Domitian against a revolt on the Rhine led by Antonius Saturninus. In September 96, Domitian was succeeded by the old and childless Nerva, who proved to be unpopular with the army. After a brief and tumultuous year in power, culminating in a revolt by members of the Praetorian Guard, he decided to adopt the more popular Trajan as his heir and successor. Nerva died in 98 and was succeeded by his adopted son without incident.

Trajan's extensive public building program reshaped the city of Rome and left numerous enduring landmarks such as Trajan's Forum, Trajan's Market, and Trajan's Column. Early in his reign, he annexed the Nabataean Kingdom, creating the province of Arabia Petraea. His conquest of Dacia enriched the empire greatly, as the new province possessed many valuable gold mines. Trajan's war against the Parthian Empire ended with the sack of its capital Ctesiphon and the annexation of Armenia, Mesopotamia, and (possibly) Assyria. In late 117, while sailing back to Rome, Trajan fell ill and died of a stroke in the city of Selinus. He was deified by the Senate and his cousin and successor, Hadrian, whom Trajan had supposedly adopted while on his deathbed. According to historical tradition, Trajan's ashes were entombed in a small room beneath Trajan's Column.