The First Samnite War lasted from 343 to 341, and resulted in Roman control of northern Campania. It was provoked by a Roman alliance with Capua, and did not go well from the Romans, who managed to disaffect their Latin allies without making any military gains.
The Second Samnite War consisted of two phases, 327-321 and 316-304. In the first part, the Romans attempted to encircle the Samnites, but were trapped at the Battle of the Caudine Forks and forced to surrender. The Roman resumed hostilities in 316 but were defeated again, in 315 at the battle of Lautulae. Their next strategy was to establish colonies and build the Via Appia to improve access to Capua, and in the end even the Samnite attempt to bring in the Etruscans did not prevail.
The Third Samnite War lasted from 298 to 290. The Samnites again formed an alliance with the Etruscans, and added the Gauls, but in the battle of Sentinum in 295, the Romans defeated the combined force.
Livy is our primary source for the entire conflict with Samnium. Although he describes the wars and battles with enthusiasm and detail, the historicity of much of the account remains suspect.