The Gregorian calendar
Pope Gregory XIII is best known for commissioning the Gregorian calendar, initially authored by the physician/astronomer Aloysius Lilius and aided by Jesuit priest/astronomer Christopher Clavius, who made the final modifications. This calendar is more accurate than the Julian calendar, which treats each year as 365 days and 6 hours in length, even though the actual length of a year is slightly less (365 days, 5 hours, and 49 minutes). As a result, the date of the vernal equinox had slowly, over the course of 13 centuries, slipped to 10 March, while the computus (calculation) of the date of Easter still followed the traditional date of 21 March. Clavius verified this phenomenon.
Gregory subsequently decreed, by the papal bull Inter gravissimas of 24 February 1582, that the day after Thursday, 4 October 1582 would be the fifteenth, not the fifth, of October. The new calendar replaced the Julian calendar, which had been used since 45 BC. Because of Gregory's involvement, the new calendar came to be known as the Gregorian calendar and has been almost universally adopted.
Much of the populace bitterly opposed this reform; they feared it was an attempt by landlords to cheat them out of a week and a half's rent. However, the Catholic countries of Spain, Portugal, Poland-Lithuania, and the Italian states complied. France, some states of the Dutch Republic and various Catholic states in the Holy Roman Empire and Switzerland (both countries were religiously split) followed suit within a year or two. Austria and Hungary followed in 1587.
However, more than a century passed before Protestant Europe accepted the new calendar. Denmark-Norway, the remaining states of the Dutch Republic, and the Protestant states of the Holy Roman Empire and Switzerland adopted the Gregorian reform in 1700–01. By that time, the calendar trailed the seasons by 11 days. Great Britain, its American colonies and Ireland adopted the reformed calendar in 1752, where Wednesday 2 September 1752 was immediately followed by Thursday 14 September 1752; they were joined by the last Protestant holdout, Sweden, on 1 March 1753.
The Gregorian calendar was not accepted in eastern Christendom for several hundred years, and then only as the civil calendar.