The Romans had lots of battles, but there were 3 most important battles ever.
The first battle was the battle of Cannae. The battle was with the 80,000 Roman soldiers against 50,000 Carthaginian troops. The Romans had lost more than half of their army, but they built up a new one and won the war ( even though they lost the battle of Cannae ). It was important because it was a key battle against the Carthaginian army.
The second battle was the battle of Alesia. The battle was between 70,000 Romans versus 80,000 Gauls, and a relief army of 250,000 Gauls. The Gauls were besieged by the Romans, and they surrendered after the relief army made 3 attempts to free the men that were besieged. Alesia was an important because after that the Gauls were defeated.
The third battle was the battle of Adrianople. The battle was with 15,000 Romans led by Emperor Valens versus 20,000 Goths. The battle was lost by the Romans; they were totally defeated by the Goths. Valens, the Emperor, was killed in battle. It was an important battle because the Roman’s treaty with the Goths was broken.
These three battles made changes in Roman History.