The Hindu or Indian calendar is based on a lunar cycle (the waxing and waning of the moon, or the moon's orbiting), while the Gregorian Christian or American calendar is based on a solar cycle (the earth's rotation around the sun). In order to match the lunar and solar cycles, about every 2 1/2 years an extra or intercalary month (adhik-maas or purushottam-maas) is added to the Hindu calendar. This addition repositions the months so that they come around the same season (thus called the LuniSolar calendar).

          Each lunar month consists of the bright phase (shukla or sud) where the moon waxes or grows, and the dark phase (krishna or vad) where the moon wanes or gets smaller. The 11th day of each half-month is designated as ekaadashee (or upavaas or agyaaras, when fasting is done). The 12th day is called baaras or dvaadashi. The 15th day of the bright phase is called poonam or poornimaa ("full moon"), and the 15th day of the dark phase is called amaas (when the moon is not visible or "new moon").

          The zero or starting point of the Hindu calendar is 56 to 57 BCE, dating the year of the coronation of king Vikram of Ujjain. The first day of the year begins with the month of Chaitra (General Indian calendar), or Ashadh (Saurashtra calendar, used in the Vachanamrut - ref. Gadhada First 77 and 78), or Kartik (Gujarat calendar, used in Swami Ni Vato - ref. 6/255).

          All three of these calendars are called Amanta Lunisolar calendars because they run from new moon to new moon. Alternatively, when the lunar month runs from full moon to full moon, it is called a Purimanta calendar.

Comparative Table of Indian and American Months and Seasons

Hindi Names of Indian Months:
Posh = Paush
Maha = Magh
Fagun = Falgun
Chaitra
Vaishakh = Vaisakh
Jeth = Jyaisth
Ashadh
Shravan = Sravan
Bhadarvo = Bhadrapad
Aso = Asvin
Kartik
Maghshar = Margasirsh

Adhik and Kshay Months in the LuniSolar Calendar
The addition of an intercalary month is done as follows: When two new moons occur within one solar month, then two lunar months occur with the same name. The first lunar month of the two is prefixed with the title adhik or mal and is considered as the intercalary month. The second one starting from the next new moon is prefixed suddh and this latter month is considered to be the true or normal month.
The months of Maghshar, Posh, and Maha are shorter in the solar calendar - so it may happen that one of these months will not have a new moon. Hence, that month is removed from the LuniSolar calendar. This is called a kshay (or missing) month. When a kshay month occurs there will always be two adhik months, one before and one after the kshay month.

Tithi and Taarik
Tithi is generally used to refer to the day of the LuniSolar month. It is defined as the time required for the longitude of the moon to increase by 12 degrees over the longitude of the sun. Thus there are 30 tithis in one month (15 in the bright phase and 15 in the dark phase).
As the motion of the moon is not steady, the duration of the tithi may vary from about 19.48 to 26.78 hours. Because of this, a tithi period may cover two successive sunrises or may not cover a sunrise at all. When this happens, there is a break in the counting of the tithis: a tithi is omitted (kshay day) or extended over two days (adhik day). Because the time of sunrise is determined by the time zone, the particular time zone may omit or add the tithi.
Taarik refers to the corresponding American day.