Martian Cycle (MC)
The problems of a calendar for Mars have been something that has been considered since the late 19th century. With the foundation of the first colony, a local calendar became paramount. In the end, the launching agency, NACSA (North American Continental Space Agency), chose to adopt a calendar such that all observations of Mars would be after Year 0.
The difficulty with the calendar is due to the fact that the length of the equinoctial year varies. However, after some calculation, the intercalcary (leap) weeks vary very slowly over time, means that every even year from 0 to 39 and every odd year from 40 to 76 of a 76 year cycle have an extra leap week.
The calendar itself is 95 weeks of 7 days, 96 on a leap year. The same day of each month is going to be the same weekday, and there are 24 months of 4 weeks (3 on a non leap-year).
Adoption and Use
Day 1 of the calendar was originally set to be the epoch 11 March 1609. This predated the first observations of Mars by Gallieo, although this later became a point of controversy between the North American Compact and the Chinese Federation. Accurately pointing out they knew about from the Zhou Dynasty (~1045 BCE), the epoch was redated to 1045 BCE to avoid any dating issues. Therefore, the first proposed landing on Mars, 21 October 2080 CE 1923 EST would become 1 Aquarius 1659 MC 1226 MTC. However, the landing crew felt that it was just plain silly to start the day 1 calendar in the year 1659, as such, the calendar starts at landing.
Despite a few starts at a different calendar, the calendar was maintained until The Fall of Earth. At that point, the Martian cities went dead silent, and by the time ships from out-of-system could arrive, they found just destruction. Unlike Venus, however, Mars required no maintenance work to be habitable. However, the Holy Protectorate of Sol would not allow it.
(ETA: Fixed Terra -> Sol, date error on the epoch listed.)