According to Sefer Yetzirah, each month of the Jewish year has a letter of the Hebrew alphabet, a zodiac sign, one of the twelve tribes of Israel, a sense, and a controlling limb of the body that correspond to it.
Elul is the sixth of the twelve months of the Jewish calendar (counting from Nisan).
It is called "the month of repentance," "the month of mercy," and "the month of forgiveness." Elul follows the two previous months of Tamuz and Av, the months of the two great sins of Israel, the sin of the Golden Calf and the sin of the spies.
The four letters of the name Elul are an acronym for the initial letters of the phrase in the Song of Songs (6:3): "I am to my beloved and my beloved is to me." "I am to my beloved" in repentance and consummate desire to return to my soul-root in God. "And my beloved is to me" with Divine expression of mercy of forgiveness.
This is the month that "the King is in the field." All can approach Him, and He shines His countenance to all.
Elul is the month of preparation for the high holy days of Tishrei. It is the month that Moses ascended to Mount Sinai a third time for a period of forty days from Rosh Chodesh Elul to Yom Kippur, when he descended with the second tablets of the covenant. These days were days when God revealed to the Jewish people great mercy.
In "small numbering," Elul = 13, alluding to the 13 principles of Divine mercy that are revealed in the month of Elul.
Letter: Yud (י)
The yud is the first letter of the Tetragrammaton, G-d's essential Name Havayah, the Name of mercy. It is also the final letter of the Name Adnut, the Name which enclothes the Name Havayah to reveal and express it to the world. Thus, the yud is the beginning (of the essence of Divine mercy, Havayah) and the yud is the end (of the manifestation of Divine mercy, Adnut).
All created form begins with an essential "point," of energy and lifeforce, the point of the letter yud. The end of the creative process is as well a "point" of consummation and satisfaction, a yud. "In the beginning G-d created…" is the initial point; "and G-d concluded on the seventh day…" is the final point.
The word yud means "hand." Our sages interpret the verse: "Even My hand has founded the earth, and My right hand has developed the heavens," that "G-d stretched out His right hand to create the heavens and stretched out His left hand to create the earth." The right hand is the point of beginning; the left hand is the point of end.
In the above quoted verse, the left hand (referred to as "My hand" without any definite designation of right or left) appears before the right hand. This accords with the opinion of Hillel that "the earth preceded [the heavens]." The earth represents the consummation of Creation–"the end of action is first in thought."
The yud of Elul is, in particular, the left hand, the controller of the month's sense, the sense of action and rectification. This is the final point of Creation reaching its ultimate purpose and end, the yud of Adnut perfectly reflecting in created reality the yud of Havayah.
Mazal: Virgo (betulah, the virgin)
The betulah symbolizes God's beloved bride, Israel, the bride of the Song of Songs who says to her groom "I am to my beloved and my beloved is to me."
The word betulah appears for the first time in the Torah (and the only time in description of a specific woman) in praise of our matriarch Rebeccah, before her marriage to Isaac.
In Kabbalah the union of Isaac and Rebecca symbolizes the spiritual service of prayer and devotion to G-d. Isaac (Yitzchak, 208) plus Rebecca (Rivka, 307) = 515 = tefilah, "prayer."
In Chassidut the verse "I am to my beloved and my beloved is to me" refers, in particular, to the service of prayer of the month of Elul.
The "virgin" of Elul (Rebecca) gives birth (retroactively, with respect to the order of the months of the year) to the "twins" of Sivan (Jacob and Esau, the sons of Rebecca, as explained above). The first tablets, given in Sivan, were broken (because of sin). The second tablets, given to Moses in Elul (the month of repentance) are whole. Repentance is identified in Kabbalah with "mother" (in general, and Rebecca in particular). "Mother" is binah = 67 = Elul.
In Kabbalah, the "mother" remains forever (on the spiritual plane) a "virgin." In a continual state of teshuvah and tefilah her "ever-new" union with "father" never ceases–"two companions that never part." With the coming of Mashiach such will be the state of the lower groom and bride. ("Father" and "mother" correspond to the first two letters of Havayah –"the higher union"; "groom" and "bride" or "son" and "daughter" correspond to the second two letters of Havayah –"the lower union").
The betulah symbolizes as well the "virgin earth," the land of Israel destined to be married to the people of Israel, as the prophet declares: "As a young man marries a virgin so will your children marry you [the land of Israel]" (Isaiah 62:5). Here we see that the children marry "mother earth" who remains "virgin earth."
The earth represents the rectification of action, the sense of the month of Elul, as described above.
Gad means "camp," as in the verse (the blessing of our father Jacob to his son Gad): "Gad shall organize [lit. camp] camps [army camps], and he shall return with all his camps" (Genesis 49:19). The special talent of Gad is to organize a "company."
The name Gad means as well "good fortune." It is truly the "good fortune" of Israel to be G-d's beloved bride, and this "good fortune" reveals itself through the means of our good deeds, especially those which are intended to rectify our blemishes and beautify ourselves, as a bride for her groom.
The "good fortune" of Gad relates, in Kabbalah, to the thirteen principles of mercy that are revealed in the month of Elul, in order to arouse the soul from its root (its "good fortune") to return to God.
Gad = 7. Gad was the 7th son to be born to Jacob. Mazal, the more common word for "good fortune" = 77. The middle letter of mazal is zayin = 7. When the two letters gimmel dalet that form the name Gad (= 7) are substituted for the zayin (= 7) of mazal, the word migdal, "tower," is formed. The verse states: "A tower [migdal = 77] of might [oz = 77] is the Name of G-d, into it shall run the tzadik and become exalted." In Kabbalah, the "tower of might" represents the bride, the betulah of Elul, the soul-root and mazal of the Jewish People. The tzadik, the groom, runs, with all of his might, to enter the "tower of might."
The sense of action is the "sense" and inner "knowledge" that through devoted deeds of goodness one is always able rectify any blemished or broken state of the soul. This is the sense necessary for the spiritual service of Elul, the service of repentance and true teshuvah to G-d. The sense of action is thus the sense never to despair. This is the "point," the yud (of Elul), of Divine service. Without it one can neither begin (an act) or end.
The sense of action is the inclination to fix a broken object (to "save" a situation) rather than to throw it away.
In addition, the sense of action is the sense of organization and the sense of management of complex systems (as Gad, the tribe of Elul signifies "camps" and "company").
Of the letter yud of Elul it is said: "G-d with wisdom [the point of the yud] founded [rectified] the earth [the sense of action]."
Controller: Left Hand
As mentioned above, G-d stretched out His left hand to create the earth (and, as quoted above: "G-d with wisdom founded the earth" [Proverbs 3:19]).
The right hand (the more spiritual of the two hands, which creates the heavens–"Lift up your eyes and see Who has created these"–the inner, spiritual dimension of reality) controls the sense of sight, whereas the left (more physical) hand controls the sense of action.
The mitzvah (commandment of action) of the tefilin shel yad is performed on the left hand (the right hand puts it on the left hand, i.e. "sees" to its being performed on the left hand).
It is the left hand which touches the heart. This teaches us that all rectified action derives from the good emotions and intentions of the heart.