We are now about to celebrate the Jewish Holiday of Succot which happens in the fall, late summer. It's a holiday that cannot be celebrated here in the Holy Land in the winter or heat of summer. All of our holidays are connected with seasons of the year and agriculture. The Jewish People are not nomadic by nature, nor theology.
The Jewish Calendar is brilliant. It is lunar--each month begins with the "new moon" and ends as that cycle does. But it's not exclusively lunar, because that, like the muslim calendar, would cause the holidays to travel across the seasonal spectrum. Twelve months of the lunar calendar are a few days shorter than it takes for the earth to travel around the sun. So the Jewish Calendar gets adjusted according to the solar calendar, to guarantee that the holidays will always fall in the correct season. There's a pattern of adding an extra month periodically that was set a very long time ago. Before that, when the vast majority of the Jewish People were in the Land of Israel, we waited for an announcement that the new moon had been sighted. And when it was still terribly wintery towards the end of Adar, the Sanhedrin would add a second Adar, so Passover would be in the spring and not winter.
Jews who live abroad do not have the agricultural connections to the Holidays and prayers for rain that we have here. Proof that Islam is not connected to this Land is in its calendar which is strictly twelve months and lunar. Their holidays float around the seasons, rootless, like the nomads they are.
In the fourth century, Hillel II established a fixed calendar based on mathematical and astronomical calculations. This calendar, still in use, standardized the length of months and the addition of months over the course of a 19 year cycle, so that the lunar calendar realigns with the solar years. Adar I is added in the 3rd, 6th, 8th, 11th, 14th, 17th and 19th years of the cycle. The current cycle began in Jewish year 5758 (the year that began October 2, 1997). If you are musically inclined, you may find it helpful to remember this pattern of leap years by reference to the major scale: for each whole step there are two regular years and a leap year; for each half-step there is one regular year and a leap year. This is easier to understand when you examine the keyboard illustration below and see how it relates to the leap years above.In addition, Yom Kippur should not fall adjacent to Shabbat, because this would cause difficulties in coordinating the fast with Shabbat, and Hoshanah Rabbah should not fall on Saturday because it would interfere with the holiday's observances. A day is added to the month of Cheshvan or subtracted from the month of Kislev of the previous year to prevent these things from happening. This process is sometimes referred to as "fixing" Rosh Hashanah. If you are interested in the details of how these calculations are performed, see The Jewish Calendar: A Closer Look. (Judaism 101)