The lunar calendar, used by the Muslims and the Incas, is based on the moon's cycles. This type of calendar is based on the periodical cycles of the moon around the Earth, with each month lasting about 29 or 30 days.
Lunar - solar calendar.
This type of calendar features lunar months in to a solar year. The luni-solar year starts the new moon after the spring equinox. Normal luni-solar years have 12 months in a year. Luni-Solar Calendars are used by the Mongol Empire, which emphasizes balance and harmony between the sun ("Yang") and the moon ("Yin"). Also the Coptic, African, and the Aramaic Christians use the luni-solar calendar, so do the Jews. Luni-solar calendars are also of great popularity among astronomers over the world, as they claim that this calendar type helps them calculate new moons, and when to hold seasonal events.
No matter what calendar you use, remember that you have an extra day of fun this year which also means I have one more day this year to love you all.