Translation by Yehoshua Siskin
1. "When Adar enters, happiness increases," and it enters today. This year, 5782, is a leap year. In other words, a year in which there is Adar Aleph (that begins now) and Adar Beit, which follows and in which Purim is celebrated.
2. Why do we add another month, in certain years, to the Hebrew calendar? The Hebrew calendar is connected to both the lunar and the solar cycle. The goal is to bring them into sync since the lunar year is around eleven days shorter than the solar year. Leap years (there are 7 every 19 years) make it possible for Pesach to always be celebrated in the spring.
3. In the Babylonian calendar, a leap year included Elul Aleph and Elul Beit, sixty days of Elul. But we double the month of Adar, a month of joy. So this year, for example, we have sixty consecutive days of joy.
4. The source of the word Adar (אדר) is Babylonian, and we were accustomed to read it as two words: ’א, an abbreviation for God, and דר or dar (resides), since God is present during this month in a unique way. Our sages note that Adar was especially joyous since it was the last month in exile before our Exodus from Egypt in the month of Nissan. Adar was the last month of hardship before redemption.
5. Today, too, as on the first day of every month, we add a musaf prayer to our morning prayers, we say Hallel, that is composed of chapters from Psalms, and we add to the Amidah and Birkat HaMazon prayers the beautiful words of Ya'aleh VeYavo: "Our God and God of our fathers, may there ascend, come, reach, and be seen, accepted, and heard, recalled and remembered before You, the remembrance and recollection of us, the remembrance of our fathers, the remembrance of Mashiach the son of David your servant, the remembrance of Jerusalem your Holy City, the remembrance of all Your people the House of Israel, for well-being, grace, kindness, mercy, good life and peace, on this Rosh Chodesh."
Have a wonderful month!