Final answer:
Hannibal crossed the Alps and entered Italy in 218 BCE, during the Second Punic War. Despite several victories, he could not secure a final peace, and the war persisted until he was defeated by Scipio Africanus at the Battle of Zama in 202 BCE.
Step-by-step explanation:
Hannibal, the famed Carthaginian general, began his audacious campaign against Rome by leading his army across the Alps in the Second Punic War. This monumental event occurred in 218 BCE, during which Hannibal made his legendary crossing with 60,000 men and several war elephants. Despite the harsh conditions and the loss of most of his elephants, those that survived became a formidable force against the Roman armies. Over the subsequent years, Hannibal remained undefeated in Italy and won several crucial battles including at Trebia, Lake Trasimene, and most notably Cannae in 216 BCE. Unfortunately for Hannibal, his victories did not yield a final peace as he could not besiege the heavily fortified Rome itself and failed to turn Italy's southern peoples against Rome.
After more than a decade of conflict, the Romans adapted their strategy to guerrilla warfare, which, against conventional warfare standards, effectively contained Hannibal's movements within Italy. The Roman general Scipio Africanus later managed to cut off Hannibal's reinforcements from Spain in 207 BCE, severely weakening his army. Ultimately, Hannibal's campaign ended when he was recalled to Carthage to defend it against a Roman invasion led by Scipio Africanus himself, culminating in his defeat in the Battle of Zama in 202 BCE.