Death of King Nebuchadnezzar, the Babylonian emperor who conquered Jerusalem and destroyed the first Holy Temple 26 years earlier, died on the 25th of Adar of the year 3364 from creation. (Jeremiah 52:31)
Rebbetzin Chaya Mushkah Schneerson (1901-1988) of righteous memory, wife of the Lubavitcher Rebbe of righteous memory, was born on Shabbat, the 25th of Adar, in Babinovich, a town near the Russian city of Lubavitch, in the year 5661 from creation (1901). In an address delivered on the 25 of Adar of 1988 (the Rebbetzin's 87th birthday, and about a month after her passing), the Rebbe initiated an international birthday campaign, urging people to celebrate their birthdays and utilize the day as a time of introspection and making resolutions involving an increase in good deeds.
Links:
A biography of the Rebbetzin
On the Jewish Birthday and the birthday customs
On the Shabbat that falls on or before the 1st of Nissan, a special reading called "Hachodesh" (Exodus 12:1-20) is added to the regular Shabbat Torah reading. Hachodesh recounts G-d's historic communication to Moses in Egypt on the 1st of Nissan (2 weeks before the Exodus) regarding the Jewish calendar, the month of Nissan and the Passover offering.
Links: The Reading for Hachodesh
From the teachings of the Chassidic masters on Hachodesh
About the Jewish calendar
Haftorah in a Nutshell
This Shabbat is Shabbat Mevarchim (“the Shabbat that blesses" the new month): a special prayer is recited blessing the Rosh Chodesh ("Head of the Month") of the upcoming month of Nisan, which falls on Thursday of the following week.
Prior to the blessing, we announce the precise time of the molad, the "birth" of the new moon. See molad times.
It is a Chabad custom to recite the entire book of Psalms before morning prayers, and to conduct farbrengens (chassidic gatherings) in the course of the Shabbat.
Links: Shabbat Mevarchim; Tehillim (the Book of Psalms); The Farbrengen
“If only the Jewish People would keep two Shabbats as they should be kept, immediately they would be redeemed.” (Shabbat 118a)
In each Shabbat, there are two Shabbats: An outer Shabbat, and an inner Shabbat.
The outer Shabbat is but an entranceway, a liberation from work. The inner Shabbat is a world inside, a world of contemplation and delight.
As a bride is whisked away from the rest of the world to be only to her beloved and no one else, so Shabbat carries us out of a mundane life on earth into the arms of the divine.
We can breathe again, our shackles temporarily broken. There is no work to do, because we have left the world of work behind.
And that allows us entry to the inner Shabbat, where divine thought breathes here on earth.
So we stop, pore over the holy, mystical teachings of our masters, contemplate deeply their words, and wrap ourselves in prayer, in communion with the Knower of all Thoughts.
Keep both Shabbats and you will find yourself redeemed.