Roman coins, while not as old as Greek coins, are arguable easier to start collecting. One aspect that sets Roman coins apart from Greek coins is that the language used is latin, an therefor more familiar to the languaged used in the western world. In addition to that, the scale of the Roman Empire and influence means that there are more coins made and generally more affordable.

Coinage from the the Roman Empire is generally divided into three masin periods: Roman Republic, The Imperators and Roman Empire

Roman coins were devalued a lot over the course of  history to continue to finance their expansion. Coins started out in precious metal and became lower and lower purity over time. This also created many denominations, here are a few

Early Republic

Denarius

Sestertius  - 1/4 Denarius

Dupondius - 1/5 Denarius

As - 1/10 Denarius

Semis - 1/20 Denarius

Quincunx - 1/24 Denarius

Triens - 1/30 Denarius

Quadrans - 1/40 Denarius

Uncia - 1/120 Denarius

Late Roman

Solidus

Miliarense - 1/12 Solidus

Siliqua - 1/24 Solidus

Follis - 1/180 Solidus

Nummus - 1/1200 Solidus

These are just some of the many demoniations used at this time.