Most ancient civilizations had some sort of calendar, some very good ones. The early Romans had a calendar as well. But in Rome, politics began to affect the calendar.
During the Roman Republic, if the priests did not like someone who had been elected to power, the priests removed months from the calendar, to shorten the year. Since people could only rule for a certain number of years, that shortened their term of office. But, if the priests liked the person in power, they added months to the calender, so thier favorite rulers had longer to rule. It was a crazy system, and pretty soon, the calendar was a mess.
When Julius Caesar came to power, he decided to throw out the old calendar and invent a new one. "His" calendar was remarkably like the ancient Egyptian calendar, but of course, like all things Roman, no credit was given to an invention by another civilization. The new calendar was Caesar's calendar. The new calendar had 365 days each year for three years, and 366 days on the fourth year, just like our calendar today.
Julius Caesar named a month after himself, the month of July. When Augustus Caesar became emperor a few years later, he named the month after July the month of August, after himself. But August only had 30 days, not 31. An emperor could not have a short month. To fix that, the astronomers took a day from February and added it to August. That's why today February is the shortest month of the year!