I'm the year of the rabbit, but astronomy doesn't give a damn about that, The Gregorian Calendar is the most widely used calendar in the world today. It is the calendar used in the international standard for Representation of dates and times: ISO 8601:2004.
It is a solar calendar based on a 365-day common year divided into 12 months of irregular lengths. 11 of the months have either 30 or 31 days, while the second month, February, has only 28 days during the common year. However, nearly every four years is a leap year, when one extra – or intercalary – day, is added on 29 February, making the leap year in the Gregorian calendar 366 days long.
The days of the year in the Gregorian calendar are divided into 7-day weeks, and the weeks are numbered 1 to 52 or 53. The international standard is to start the week on Monday. However, several countries, including the US and Canada, count Sunday as the first day of the week.
Replaced Julian Calendar
The Gregorian calendar's predecessor, the Julian Calendar, was replaced because it was too inaccurate. It did not properly reflect the actual time it takes the Earth to orbit once around the Sun, known as a tropical year.
Realigned With the Sun
The Julian calendar's formula to calculate leap years produced a leap year every four years. This is too often, and eventually, the Julian calendar was several days out of sync with the fixed dates for astronomical events like equinoxes and solstices.
The introduction of the Gregorian calendar allowed for the realignment with events like the vernal equinox and winter solstice.

No. The Solar Year works best. Although it's interesting that you can fit 13 months (Moon cycles) into a solar year with just one day left over. Or two days each leap year. 13 x 28 days = 364 days.