The Maya calendar is often described as uniquely elaborate. In its essentials it was shared across Mesoamerica. What the Maya added was the habit of recording dates in permanent public inscriptions, and a long linear count that few of their neighbours used to the same extent.
Two cycles ran together. The tzolk'in of 260 days combined thirteen numbers with twenty named days. The haab' of 365 days ran eighteen months of twenty days plus a short and inauspicious remainder. Because the two lengths share a factor, any given combination recurs every 52 years, a period conventionally called the Calendar Round. The 260-day count governed naming, prognostication and ritual timing, and it is still kept by day-keepers in the Guatemalan highlands, which makes it one of the longest continuously used calendars anywhere in the world.
For dating monuments the Classic Maya used the Long Count, a tally of days from a base date falling in 3114 BCE on the correlation most scholars accept. It is not cyclical; it simply accumulates. That is why Classic inscriptions can often be placed to the day, and why the dynastic history of the period can be written at all.
The completion of a large Long Count period in December 2012 produced a substantial popular literature claiming the Maya had predicted the end of the world. They had not. Period endings were occasions for ritual and for raising monuments, Classic texts project dates far beyond 2012, and the damaged inscription usually cited in support of the claim says a good deal less than it was reported to say. The episode is a useful illustration of how readily Maya material is made to carry meanings brought to it from outside.
Alongside the calendar ran astronomy of real precision. The Dresden manuscript contains tables tracking the cycle of Venus and the possibility of eclipses, worked out to serve ritual timing rather than pursued for its own sake.