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THE HEBREW CALENDAR (in a nutshell)
The Hebrew calendar is based, primarily, on the moon's rotation, or what is known as the lunar calendar, consisting of twelve lunar months. Each lunar month is made-up of exactly 29 days, 12 hours and 44 minutes. These numbers collected altogether amount to 354 days to each year, or what is known as "a regular year" (Heb. כסדרה), while the accumulation of 44 minutes to each lunar month amounts to nearly 9 hours in the course of a year; in two years, to nearly 18 hours, and in three years, to a little more than 26 hours, or what can be termed as an additional day. It is therefore necessary to make the addition of one 24-hour day every three years to the Hebrew calendar, turning an ordinary 29-day lunar month of Heshwan into a 30-day month, or what is known as an intercalated month, and which brings the Jewish year to 355 days. Such a year is called "a full year" (Heb. שלמה). Now since each lunar month repeats its phases, or starts anew with the mean conjunction of the sun (hence: New Moon) every 29 1/2 days, and since, for all practical purposes, it is impossible to divide a day in half, this accounts for why the twelve lunar months in the Jewish calendar are made-up of 30, 29, 30, 29, etc. days respectively, which balances out in the long run. The first of these lunar months is Nisan, as it is written (Exo. 12:2): "This month shall be unto you the beginning of months." It is made-up of 30-days.
Note that there is a difference of eleven days between a Solar Year (of 365 days) and a Lunar Year (of 354 days). The Seasons repeat themselves every twelve months. However, the seasons are governed by the earth's rotation around the sun (i.e. Solar Year) of 365 days, rather than by the moon's rotation. Here, a technical problem arises insomuch that Passover, according to a biblical injunction (Deut. 16:1), must always fall in the springtime. Since the lunar year lags behind the solar year by eleven days each year, and after three years it would lag behind the solar year by 33 days, had this process continued, Passover would have eventually fallen in the winter months. It, therefore, becomes necessary to intercalate the year by adding another month to the Hebrew calendar every two or three years, in order to keep the lunar cycle aligned with the solar cycle. This accounts for the first and second months of Adar which are added to the calendar in a Leap Year (Heb. שנה מעוברת), there being seven Leap Years in the course of a nineteen-year period. These Leap Years are repeated in their regular order every 19 years. The first Adar is always a 30-day month, while the second Adar is always a 29-day month. As for the three surplus days in the 33-day lag every three years and which were not accounted for by the addition of a 30-day month, these days are taken in by the frequencies of Leap Years occurring every 2 to 3 years (seven in a 19-year period), so that in 19 years, 210 days have been added to the Hebrew calendar by the addition of a 30-day month, making the total number of days equal to the total number of days appearing in a 19-year Solar Year (6,935 days). Complete alignment of the Solar and Lunar years are attained every 19 years, while in between these years, the two are constantly running in close proximity to each other.
The Hebrew months, in their proper order, are as follows:
Nisan = 30 days
Iyyar = 29 days
Siwan = 30 days
Tammuz = 29 days
Av = 30 days
Elul = 29 days
Tishri = 30 days
Heshwan = 29 days (30 days when intercalated, making it "a full year")
Kisleu = 30 days (29 days in "a defective year")
Tevet = 29 days
Shevat = 30 days
Adar = 29 days (In a Leap Year, the first Adar is 30 days)
 Formerly, each new lunar month was sanctified by the testimony of eye witnesses who had seen it appear in the sky.
 cf. Babylonian Talmud (Rosh Hashanah 21a); Maimonides (Mishne Torah, H. Kiddush Ha-Chodesh 4:1; 1:1-2)