The Romans had a calendar which consisted of 10 months, starting on March 1st and ending with December. In between was an unnamed winter period. The priests’ task was to determine the start of every new year. Julius Caesar introduced the Julian calendar, with 365 or 366 days, 12 months and a system with weeks. The Julian calendar was used until the late 16th century.
The Julian calendar had a leap year every 4 years. Averagely, a year was in this way counted to be 365,25 days. In reality it is a fraction shorter. This is fixed in the Gregorian calendar so that leap years do not occur on century years (divisible by 100), unless the year is also divisible by 400. For example, 1900 was not a leap year, but 2000 was.
The ‘mistake’ had gone up to 10 days of miscalculation. Therefore, Pope Gregory, the architect of the Gregorian calendar (now still in use in most parts of the world), decreed 10 days should be dropped between October 4th and 14th 1582. From that time, a discrepancy existed until in the 19th century between the Christian countries using the new calendar and the orthodox ones (like Greece in 1923 and Russia in 1917), using the old one. Some orthodox churches still go by the Julian calendar, resulting in different calculation of holidays like Easter and Christmas.
In the Middle Ages, the New Year could be celebrated at January 1st, March 1st, March 25th or simply; Easter: the first Sunday after the first full moon after vernal equinox (21st of March). Since about 1600 most countries have used 1 January as the first day of the year. Italy and England, however, did not make 1 January official until around 1750.