An explanation of the Mayan calendar:

The classic-era Maya used two systems of calendars, which are referred to by archaeologists as the Long Count and the Calendar Round.

The Long Count was a simple counter from 0.0.0.0.0.

baktun.katun.tun.uinal.k'in

baktun = 400 years
katun = 20 years
tun = 1 year
uinal = 20 days
k'in = 1 day

The Calendar round was the intersection of the religious Tzolkin calendar and the civil Haab calendar.

The Tzolkin used 20 names and 13 numbers, each in a cycle, to refer to days.  If a given day was 3 Cauac, the next day would be 4 Ahau.  This gave a 260-day cycle.

The Haab used a system much like our own; each month save one had 20 days, from 0 (the 'seating') to 19.  The last month had 5 days, 0-4.

