Since you ask for the dates of the Ancient Roman era, this answer will provide you with the earliest dates of Roman history, before it became a republic and later an empire. However, if you are in fact looking for the dates of the rise and fall of the Roman Empire, you will find those below as well.
Rome was first established in the eighth-century BC, most likely in 753 BC, though it is hard to be exact. Legend has it that the city was founded by Romulus and Remus, two abandoned twins raised by a she-wolf. In these ancient times, Rome was actually a monarchy, with Romulus taking place as its first king. Rome remained under this political structure until the establishment of the Republic in 509 BC, when King Lucius Tarquinius Superbus was overthrown by his subjects. This event marked the end of Ancient Rome and the beginning of the Early Republic, which itself lasted until the rise of the Roman Empire.
The Roman Empire began in 27 B.C. after the senate gave the title of "Augustus" (venerable, worth of grace) to Julius Cesar Octavianus. This was known as the period of the Julio-Claudians. Hence, this will be first emperor that will be succeeded by perhaps the four most outrageous emperors. Their quick secessions ended in the year 68-69 A.D. The four emperors were Tiberius, Gaius Germanicus, alias "Little Boots" or "Caligula", Claudius, and Nero. After the fall of Nero's regime came the Flavians (69-96 A.D.).
After the civil wars, the Favian dynasty began with Vespasian who was succeeded by his sons Titus and Domintian. Domintian was assassinated in 96 A.D. which led to the Age of the Antonines known as "The age of the five good emperors".
This era is ruled by Nerva, Trajan, Hadrian, Antoninus Pius, the author of the famous Meditations, Marcus Aurelius, Lucius Verus and Commodus This period lasted from 96 A.D to 193 A.D. after Commodus's assassination.
In came the Severians in 193 A.D until 284 A.D. which ended with the assassination of then-emperor Alexander Severus.
After this came the era of Diocletian and Constantine which witnessed the fall of Western Rome and the beginning of the Byzantine Era. Therefore, the end of the Roman empire was 476 A.D