The Capitoline Hill was long the seat of Rome's government. Earliest Rome was a kingdom with two classes, the patricians (nobles) and the plebeians (commoners). The Senate, or Council of Elders, elected the monarchs and limited their power. No plebeian could hold a rank greater than Tribune.
The Italian Peninsula was occupied by many powers, which aided Rome in a way, as it was easy to divide and rule, take advantage of Wars between powers, or intimidate weaker powers. The Carthaginian Empire centred in the city of Carthage (in modern day Tunisia) was the greatest Military and Commercial Power in the Region but long underestimated the power of Rome, it controlled the Western Mediterranean Coastal regions of North Africa, Spain, Sardinia, and Western Sicily including Palermo. Mediterranean means Middle Earth Sea, the Romans called it Mare Internum.
The Etruscans occupied the land north of Rome including Pisae and Firenze (Florence), Barbarian Celts were further North at Genoa and elsewhere. The Apulians occupied the South-eastern coastal region at such places as Bari, Brindisi (a modern Commercial Port), and Tarantus (a modern Naval Base). Sannitians centred around Neapolis (Naples), and the Greek City States controlled the rest of the South which included Syracuse and Crotone.
Syracuse a port in South-eastern Sicily, was the home of Archimedes (287-212 BC), and one of the greatest Greek Cities anywhere. Archimedes invented a device to focus the rays of the sun, this burned the sails of Roman Triremes thus putting back their invasion by two years. He also invented the Archimedes Screw a device for raising water using minimal effort still used in Egypt today. And said Eureka - I've found it, when trying to solve a problem, where a goldsmith had substituted silver for gold in the King's crown. He worked out in his bath that he could measure the volume by putting it in water, and measuring how much was displaced. As gold and silver have different densities, all he had to do was to weigh the crown, thus confirming the accusation. He also designed Catapults to defend the city, unfortunately they were overwhelmed by Roman numbers. He was killed by a Roman soldier when trying to protect one of his experiments, during the invasion.
Crotone, a Southern Greek Port in Italia, was once home to Pythagoras (circa. 500 BC) and his cult of numbers. This was a religion which worshipped numbers, any member giving away secrets was killed. Pythagoras did not discover the Pythagorean Triangle (a² + b² = c², for integers e.g. a=3 b=3 c=5), just promoted it. It was probably discovered in Babylonia, 1000 years before, they had a number system based on 60, which is still used by us for measurement of time and angles. Many Greeks regarded irrational numbers as unholy as they had no end. Zero was not regarded as a number, neither were negatives.
Etruscan kings ruled Rome from the 7th to the late 6th century BC, but when the last monarch was overthrown, about 510 BC, a republic was established. Rome subsequently began to absorb the surrounding areas, mostly through War, every summer Rome went to War, Warfare was impractical in Winter with the very limited Classical Technology available. After a Gallic invasion early in the 4th century BC, the so-called Servian Wall was built around the city. The first aqueduct in Rome was built in 312 BC. At the same time, the Via Appia, connecting the city with southern Italia, was constructed.
Rome continued to grow during and after the Punic Wars with the Carthaginians (264-146 BC). There were three Wars, the first was when the Romans occupied Western Sicily, the second involved them seizing Eastern and Southern Spain, and finally Carthage was taken.
The legendary Hannibal, lead his Elephants, across Africa, Spain, Gaul, and the Alps to fight the Romans on their own soil. The battle of Cannae in southern Italia pitting two Roman Consular Legions lead by Varro of 65,000 legionnaires and 7,200 cavalry against Hannibal's 32,000 infantry and 10,000 cavalry. Not only did Hannibal win but virtually all the Romans were wiped out, with loses of only 10,000 on his side. For centuries to come the refrain of Hannibal ad Portas! - Hannibal is at the gates, was using to frighten little children.
After this disastrous defeat the Romans avoided engaging Hannibal in battle on equal terms, instead trying to destroy his base and sources of supply. While also trying to crush a Greek rebellion in the South. The final War pitted the Roman General Scipio Africanus (then known as Publius Cornelius Scipio), against Hannibal. He started his war by capturing Carthage's Spanish Provincial Capital. An armistice, was agreed which he broke allowing him to launch a surprise attack on Carthage, the battle of Zama. In desperation Hannibal was recalled from Italia. Hannibal mustered 45,000 infantry (many raw recruits) and only 3,000 cavalry against 34,000 legionnaires and 9,000 cavalry. The superior number of cavalry and veteran troops gave Scipio victory.
Carthage's inhabitants where sold into slavery, and the site was salted so nothing could ever grow there again. Slavery was a major reason for the expansion of the Empire, every time an army was defeated, it's members and many of the local population could be sold into slavery, at a vast profit. Italia had an insatiable demand for slaves, to work on estates growing grain and grapes (for wine), their average life expectancy was 7 years, although house slaves lived under better conditions and could sometimes earn their freedom. It was a close fight, and Carthage could easily have won, which would have drastically altered history.