I may be reading it wrong, but it almost seems like you're implying that the Greek empire was the direct predecessor to the Roman, which isn't the case. The breakup of Alexander's empire is called the Hellenistic period, which basically divided the empire into separate kingdoms ruled by his generals. It was after this that the Romans came in and conquered Greece.

As /u/JP-Marat said, seems like you are saying the greek empire was the predecessor to Rome. Not the case. You are correct that it was multiple leaders over time who conquered and expanded the Roman frontier. It would be impossible to list it out here, and I am far from qualified to do so despite my love of Roman History. The good news for you though is the Roman Republic, and Empire, is one of the most documented and well researched parts of antiquity! I would suggest you go and get an easy to read over view of the history. Something super approachable and not very dense. That should give you a good basic introduction. From there, pick out parts of Roman History you are interested in. I guarantee you there are multiple books, academic or casual, covering that period for you to delve deeper into. Alternatively, search on this sub for anything containing the word "Roman", you'll probably find some very interesting stuff. For instance, https://np.reddit.com/r/AskHistorians/comments/2pvxsr/the_decline_and_fall_of_the_roman_republic_ama/

If you are really interested in Roman history, you are in luck! It is one of the richest periods of history to learn about. Have fun!