David, a descendent of Judah the son of Jacob as well as of Ruth, a Moabite convert to Judaism, was anointed King of Israel by Samuel in 878 BCE. All future legitimate kings of Israel were David's descendents, as will be Moshiach (the messiah), who will "restore the kingdom of David to its glory of old."
David fought many wars, defeating Israel's enemies and securing and expanding its borders. He conquered Jerusalem, purchased the Temple Mount from its Yebusite owner, and prepared the foundation for the Holy Temple (which was built by his son, King Solomon). David served as the head of the Sanhedrin and the foremost Torah authority of his generation; he is also the "sweet singer of Israel" who composed the Book of Psalms that for 28 centuries has embodied the joys, sorrows and yearnings of the Jewish people.
King David passed away on Shavuot of the year 837 BCE, age 70. (While some say it was on Sivan 6, according to many it was on Sivan 7.)
Links: King David
Avraham ben Avraham, the famed "Ger Tzedek" (Righteous Convert) of Vilna, was born as Valentin Potozki, the son of Count Potocki, one of the richest landowners in Poland. As a student in Vilna he discovered Judaism and decided to convert -- a capital offense in most countries in Christian Europe at the time. He fled to Amsterdam where he secretly converted to Judaism, assuming the name Avraham ben Avraham ("Abraham the son of Abraham").
Years later he returned to Vilna, where he was eventually recognized as the missing son of Count Potocki and arrested by the church. He refused to renounce his faith and was sentenced to death. He was burned at the stake in Vilna on the 2nd day of Shavuot of 1749.
Link: The Ger Tzedek of Wilno
Outside of the Land of Israel, Shavuot is observed for a 2nd day today.
Links: Shavuot
Yizkor, the remembrance prayer for departed parents, is recited today after the morning reading of the Torah.
Links:
The Yizkor Prayer
Honor Due to Parents
On Breavement and Mourning
Once a month, as the moon waxes in the sky, we recite a special blessing called Kiddush Levanah, "the sanctification of the moon," praising the Creator for His wondrous work we call astronomy.
Kiddush Levanah is recited after nightfall, usually on Saturday night. The blessing is concluded with songs and dancing, because our nation is likened to the moon—as it waxes and wanes, so have we throughout history. When we say this blessing, we renew our trust that very soon, the light of G‑d's presence will fill all the earth and our people will be redeemed from exile.
Though Kiddush Levanah can be recited as early as three days after the moon's rebirth, the kabbalah tells us it is best to wait a full week, till the seventh of the month. Once 15 days have passed, the moon begins to wane once more and the season for saying the blessing has passed.
Links:
Kiddush Levana: Sanctification of the Moon
Brief Guide to Kiddush Levanah: Thank G‑d for the Moon!
Torah is the interface between the Infinite and creation. On the outside, it speaks the language of humankind. On the inside, it is depth without end.
Grasp either end and you have nothing. Grasp both and you have G‑d Himself.