From Innerpedia - Encyclopedia of Torah's Inner Dimension - Chassidut and Kabbalah
Adni אֲדֹנָ־י (pronounced Adni) is one of the Names of God appearing explicitly in the Bible.
The Name Adni, literally means “my master.”
In Kabbalah, Adni is associated with the sefirah of kingdom.
The Name Adni acts as a garb, a revelatory vessel, for the essential Name Havayah. The relationship between these two Names of God was first alluded to in God’s words to Moses at the Burning Bush: “This is My Name forever and this is My Remembrance from generation to generation.”<ref name="exodus">Exodus 3:15</ref> “My Name” refers to the Name Havayah, while “My Remembrance” (which can also be read as “My Enunciation“) refers to the Name Adni. From this we learn that we are to pronounce the Name Havayah as Adni in prayer or when reciting a verse of the Torah.
The Name Adni (representing God’s immanence) serves to reflect the Name Havayah (representing God’s transcendence) as it manifests itself in the created dimensions of time and space.
Relationship with the sefirah of Kingdom
Using the Atbash transformation, Adni transforms to תקטמ, whose value is 549 or 9 • 61. 61 is the gematria of “I” (אָנִי), the most common connotation for kingdom. Kingdom is defined as possessing nothing of itself, and is formed exclusively from the 9 sefirot of kingdom belonging to the sefirot above it (in Ze’er Anpin). The kingdom of wisdom becomes its wisdom, the kingdom understanding becomes its understanding, etc.).
The sefirah of kingdom is identified with the Aramaic language in general, because Aramaic is considered the backside of Hebrew, the holy language, making it the language of translation. For this reason, the sages refer to Aramaic as simply “translation” (תַּרְגוּם, pronounced targum). The filling of Adni is אלף דלת נון יוד. Its value is 671, which is the gematria of the Aramaic word for “gate” (תַרְעָא). Kingdom and the power of its Divine Name, Adni, represent the gateway for entering into the mystery of the sefirot and the rectified consciousness of One.
Relationship with Havayah
A central kavanah in Kabbalah involves a holy Name created by combining the 4 letters of Havayah and the 4 letters of Adni, alternately.
When the first letter is the yud of Havayah and the final letter the yud of Adnut (יאהדונהי), this Name represents the higher unification (יִחוּדַא עִילָאָה) by which created time and space are elevated to unite with God's transcendent nature that is above time and space.
When the first letter of the resulting Name is the alef of Adni and the final letter (אידהנויה), the hei of Havayah, the Name represents the lower unification (יִחוּדַא תְתָאָה) by which God's transcendent aspect unites with His immanent aspect, manifest Himself as the continual Creator of time and space.
Numerically, both the value of Havayah (26) and the value of Adni (65) are multiples of 13. When the two are combined, the sum is 91, the value of the word “Amen” (אָמֵן) and 13 (the sum of integers from 1 to 13).
The sum of the four primary fillings of Havayah is 232. When we add this to 671, the sum comes to 903, which is the 42, the number associated with Creation. 903 is also the product of 7 and 129, where 129 is the value of "Havayah is Elokim" (י-הוה הוּא הַאֶ-לֹהִים, the phrase we repeat 7 times at the conclusion of the Ne’ilah service of Yom Kipur.
The values of Havayah (26) and Adni (65) are both square plus 1 numbers.