There is no absolute calendar, but many of them.

I. The lunar calendars:

The year is composed by 12 months of alternatively 30 and 29 days, which give a year of 354 days. Because of the 11.25 days diference with the solar year, the months ramble quickly between the seasons.

Example: The muslim calendar

It exists since the year 632 of the christian era, wich means a lot of time before the Revolution and the Republican calendar, a lot of time before the so good shaving of Louis XVI. The first day of the year 1 (the Hégire) corresponds to July16, 632. It's a purely lunar calendar.

The average duration of the moon period is of 29 days, 12 hours, 44 minutes and 2.8 seconds. It exceeds the duration of the muslim month by about 44 minutes, or about 11 days for 30 years. So, the muslim calendar is composed by 19 years of 354 days and 11 years of 355 days (the abundant years).

II. The solar calendars:

They are based ont the tropic year duration, which means the lapse of time between two spring equinoxes, or 365.2422 days.

The julian calendar was adopted by Julius Ceasar in 45 before the christian era, a lof of time before the Republican calendar and the attempt to reduce the powers of the monarchy, beginning by the head.The julian year has a duration of 365.25 days. It exceeds the tropic year by 11 minutes and 14 seconds.

The gregorian calendar was born in 1582, a year in which the spring equinox occured on march 11, by the sweat of Julius Ceasar, who was quite ahead of time. On this year, the pope Grégoire XIII instigates a new calendar to correct the errors of the problems caused by the irreducible Roman. (In fact, Julius Ceasar had been reduced to silence in spite of his irreducibility — Tu quoque, mi filii!). The year passed directly from thursday, October 4, 1582 to friday, October 15, 1582. 11 days disappeared in the twilight zone. The gregorian year duration is of 365.2425 days:

This means that a day is added every four years (the leap years), one day is rested from the secular years wich had to be leap (for instance, 1900 wasn't a leap year in spite of being a multiple of 4). To end, all the secular years multiple of 400 are leap years (400, 800, 1200, 1600, 2000, 2400...)

The gregorian year exceeds the tropic year by 0,0003 days, about 3 days for 10 000 years

The republican calendar is also a solar calendar, but it's more much fun than the others.

III. The lunar-solar calendars

They are established on the Méton cycle: he was an astronom of Athens in the V century before J.C. (Jesus-Christ, not Julius Ceasar): 19 solar years of 365.25 days correpond to 235 lunar periods, with an error of about 1h30. From time to tim, a 13th month is added, to force the beginning of the year to take place always in the same season. The 19 years cycle is composed by 12 ordinary years and 7 embolismic years.

The ordinary year is a year of 12 months of alternatively 29 and 30 days, which gives 354 days.

The embolismic year is a year of 13 months of alternatively 29 and 30 days, which gives 384 days.

Examples of lunar-solar calendars: the jewish calendar and the chinese calendar (this on till 1911)