The first war between 264 BCE to 241 BCE when Rome wanted to expand its territory beyond the Italian Peninsula to gain control of shipping lanes. But were controlled by Carthrage which triggered the first row.
In the second war was between 218 BCE and 201 BCE when a leader called Hannibal tried to take over Rome when he conquered the Italian peninsula. Rome then forced his army to retreat to Nourth Africa which was where the Roman general Scipio Hannibal.
The third war was between 149 BCE to 146 BCE when Carthrage started to get some of their power back. Rome responded to this and attack Carthrage, defeating the city.