The knowledge we have on the roman calendar are quite inaccurate, various debates still exist on it. This article aims at giving only the mainlines of this antic calendar.

Roman calendar is essentially a lunar calendar, but it aims also at being synchronized with solar year. Indeed, at the origin, each month starts with a new moon and each year starts after march equinox. According to the tradition it is introduced at Roma foundation in 753 BC It is the referring calendar in all the roman empire until the Julian calendar introduction in 45 BC by Julius Caesar. It has been submitted to a set of major reforms during its lifetime.

Still according to the tradition, the roman year has 10 months of either 30 or 31 days: Martius (31 days), Aprilis (30 days), Maius (31 days), Iunius (30 days), Quintilis (31 days), Sextilis (30 days), September (30 days), October (31 days), November (30 days), December (30 days).

Year last 304 days (sometimes 305). The first day of Martius starts each year at the first new moon after vernal equinox (around March 22^nd). To stick with the solar year, approximately 60 days are added in winter waiting Martius come back. Those added days are not counted in the calendar.

The Julian calendar has been introduced by Julius Caesar in 43 BC to replace the complex roman calendar. It is not really used before 45 BC.

It reuses the 12 months of the Roman calendar but changes their ordering, so year counts 365 or 366 days and looks like: Januarius (31 days), Februarius (29 ou 30 days), Martius (31 days), Aprilis (30 days), Maius (31 days), Junius (30 days), Julius (31 days), Sextilis (30 days), September (31 days), October (30 days), November (31 days), December (30 days). This configuration seems the most obvious but is nevertheless submitted to debate by historians.

Year starts now with January. Month Intercalis is forgiven. Instead, one day is added in February every 4 years (the rule is not so regular the first years of the calendar usage). The years having one additional day are the leap years. We can note that the seventh month Quintilis, is renamed Julius in honor of Julius Caesar.

For a not well known reason, at the beginning of the Julian calendar, the intercalaris days are inserted every 3 years instead of 4. In order to cancel the error, Emperor Augustus decided in 8 BC that none of the years between 9 BC and AD 8 (or 12 according to some inputs) are leap years. Then leap years are regularly set every 4 years.

In memory of Augustus and his reform, Sextilis moth is renamed Augustus. Considering that Augustus's month cannot be shorter than the one of Julius, Augustus has been increased to 31 days, implying the re-configuration of the year such as it looks like today.

The Gregorian calendar is the calendar in use nowadays, in most of the occidental countries and through the world.

It has been introduced during the XVI^th century by Pope Gregory XIII (1502 - 1585) to correct the inaccuracies of the Julian calendar. The main problem was that Easter day, which is computed from vernal equinox, drifts each year a little bit compared to the solar year. To get around this, the Julian leap year rule is modified, so the years divisible by 100 are not leap years whereas the ones divisible by 400 are.

The day of its introduction varies a lot from country to country. The first countries to apply it in 1582 October the 15^th, were Spain, Portugal and the states of Italian peninsula. The day of its introduction, some days have been removed from the current Julian date in order to correct the accumulated drift throught the ages. The last countries to apply it were several west, central and south African states.

The Gregorian calendar keeps the same months and day of the week than the Julian calendar.

The Gregorian calendar is traditionaly used inside Anno Domini system. That's why it usually has no year 0, but this rule is not invariant following the used reference era.

The French calendar is one of the most emblematic reform of the 1792 French revolution. It aims at breaking the relations with the past such as christianise.

French calendar has 12 months of 30 days. They are named: Vendémiaire, Brumaire, Frimaire, Nivôse, Pluviôse, Ventôse, Germinal, Floréal, Prairial, Messidor, Thermidor, Fructidor to remenber the cycle of the seasons. Year starts around September the 22^th at automnal equiniox. Five feast days follow Fructidor month. A sixth day, day of the revolution, is added the leap years.

It has been introduced 1793 September the 22^nd directly at year 2. In consequence, year 1 which designates the fundation of the french republic, has never existed.

The first years of the calendar, leap years were computed according to the vernal equinox, without following any predefined rule. The aim was to start each year with the solar year. So, years 3, 7, 11, 15 et 20 were leap years.

As the exact day of the vernal equinox is not easy to compute, this system has been abandoned in favour of the old system in use in Gregorian calendar. The application of this reform was planned in year 20, but unfortunately never been used because the French calendar has been definitively abolished in 18 and replaced back by the Gregorian calendar.

The indian civil calendar, also known as indian national, was introduced by the Calendar Reform Committee in 1957. Years are counted in the Sake era. It is offically used on March 22^nd 1957, Chaitra 1^st 1879 of the Saka era.

The years in the indian civil calendar are divided in 12 moths, following the structure: Chaitra (30 ou 31 days), Vaisakha (31 days), Jyaistha (31 days), Asadha (31 days), Sravana (31 days), Bhadra (31 days), Asvina (30 days), Kartika (30 days), Agrahayana (30 days), Pausa (30 days), Magha (30 days), Phalguna (30 days). Chaitra, the first month of the year, has 31 days in leap years and 30 in normal years. The names of the months derived from the older Hindu lunisolar calendars.

For simplification reasons, the way leap years are computed in the civil indian calendar is the same as in gregorian (The computation rules must be applied to the gregorian year, so Saka year + 78 years). Therefore, the offset between the two calendars is constant. The indian civil year always starts on gregorian March 22^nd the non leap years and March 21^st the leap years.

The week of the indian civil calendar is equivalent to the gregorian one. Thus, a regular seven days cycle. The days of the week are named: Raviãra (Sunday), Somavãra (Monday), Mañgalvã (Tuesday), Budhavãra (Wednesday), Guruvã (Thursday), kravãra (Friday), Sanivãra (Saturday).

The Julian period starts January 1^st 4713 BC (Julian calendar) and ends December 31^st AD 3267, 7980 years latter. It has been invented by Joseph Justus Scaliger (1540;1609) and is defined as a 7980 years cycle in which days happen the same day of the week, moon phase within the same solar cycle.

Note: The Julian period is different than Julian calendar.

Julian day numbering (JDN) system is directly derived from the Julian period. Julian days is the count of days since starting point of the Julian period. So, day 0 corresponds to January 1^st 4713 BC, day 2 corresponds to January 2^nd 4713 BC, and so on. This system allows to identify any historical facts independently from calendars. The first Julian period is defined so all known historical events are contained in it. The system eases date conversion from calendar to calendar.