How many wars were fought in the punic wars?

There were three Punic Wars.

The first was fought from 264-241 BC, mainly over the island of Sicily. Rome ended the land phase of the war by defeating Carthage at the Battle of Agrigentum in 262, and eventually won the naval phase of the war as well. As a result, Rome gained control over Sicily, and, in the aftermath of the war, seized Sardinia and Corsica as well.

The Second Punic War, fought from 218-202 BC, began in Spain. The Carthaginians, under Hannibal, crossed the Alps and invaded Rome. He was unable to take the city, due to his lack of siege equipment, and resorted to plundering the Roman countryside. Rome, in return, resorted to invading the city of Carthage. Hannibal retreated to defend his homeland, but was defeated in 202 at the Battle of Zama. This marked the end of Carthage's reign as a major power.

The Third Punic War was fought from 149-146 BC. It was a fairly minor war which resulted in the absolute destruction of Carthage.