First Punic War 264 - 241 BC:
Carthage was a city in North Africa. It was very similar to a Greek city-state by 300BC. It was a wealthy city-state that made most of its money from trade. Carthaginian merchants went from one end of the Mediterranean to the other. The city's fleet was huge, and its army was one of the best in the ancient world. These merchants traded in the western Mediterranean where only Greeks traded before. They also traded a far north as England to get Cornish tin, and down the coast of western Africa to get gold and ivory.
Like Rome, Carthage used the people they conquered as part of their army. They also used mercenaries, which Rome did not do. By the early 200's BC, Carthage had an empire that controlled not only north Africa but they also controlled Sicily, Corsica, Sardinia and other small islands in the western Mediterranean.
Carthage had become the largest and richest state in the western Mediterranean and this caused Rome to become worried as the island of Sicily, which Carthage controlled was just off the coast of Italy.
What actually was the cause for Rome and Carthage to become rivals had not only to do with trade but with the conflicts of another city-state. Messena, a port city on Sicily had a dispute in 264 BC. Messena was the city that controlled the straits near Italy. There were two sides in Messena and they had a disagreement. The dispute had to do with charging a tax on outside trade. One side of Messena wanted a tax and the other side did not think it was necessary. One side Carthage for help.
Carthage sends its fleet to Messena. Rome sees this action as a threat to their dominance in the Mediterranean,