The entire structure of tikkun presupposes an original primordial rupture. Sefer Etz Chaim 1:1-5 describes how the Ein Sof contracted Itself to produce a void, the first act that made differentiated worlds — and therefore the need for their repair — possible; and Sefer Etz Chaim 18:1-7 then specifies that three dimensions of that rupture — including the vessels that shattered and fell into the world of Beriah — each require their own mode of rectification through a process of spiritual gestation.
The breaking of the vessels is the engine of tikkun in the Lurianic reading of cosmic history: Sefer Etz Chaim 8:1-4 describes how the kings who died required rectification through the arrival of a ruach that revived them, a process identified with the mystery of the upright human form, the name of forty-five, and the emergence of male and female as distinct — the structure of Adam being the vehicle through which shattered primordial forces are reconstituted.
The Egyptian exile is itself read as a tikkun mechanism: Sha'ar HaKavanot, Sermons on Passover 1 explains that Israel descended to Egypt — which represents the concealment clinging to the posterior of the supernal Da'at — precisely because the generation of the sin had caused the forces of impurity to draw sustenance from that damaged source, and the entire enslavement served to purify and rectify the holy sparks trapped within.
The 288 sparks scattered through the shevirah are the specific currency of cosmic tikkun, referenced by name in Sefer Etz Chaim 18:1-7, and their recovery through human action is the axis around which the Lurianic system turns; רמח"ל, אדיר במרום דף י, ועיין שם עוד elaborates that after Adam's sin deepened the corruption to the level of Ze'ir Anpin, the path of tikkun shifted to Avraham's model of toil and mitzvot, separating the dross outward — including through Yishmael and Esav — so that holiness could be restored to its place.
Observance of the 613 commandments is the primary human instrument of tikkun: Sha'ar HaMitzvot, Introduction 2 states that every soul is obligated to fulfill all 613 commandments because as long as any one of them remains unperformed the tikkun of that soul is incomplete; and Nefesh HaChayim, Gate I 22-24 adds that even when performed without intention or understanding of their inner secrets, the commandments rectify the worlds and increase holiness and light — each one ascending on its own to produce its particular effect.
Teshuvah and the High Holiday season constitute a dedicated window of tikkun for the damage wrought by sin: Likkutei Torah, Nitzavim 44c-45a explains that Rosh HaShanah through Yom Kippur is the time appointed for repairing the blemish of transgressions, comparing the process to rebuilding a house from its very foundation in order to correct a flaw in its middle — because only by renewing the entire structure from the bottom up can the damaged portion be properly restored.
Torah study is the specific medium through which blemishes of the soul are repaired at their supernal root: נפש החיים, שער ד פרק לב teaches that since every repair must occur at the upper root of the thing being repaired, and since each Jewish soul's supernal root is a letter of the Torah, all damage wrought by sin is rectified and sweetened precisely through engagement with Torah — for even a soul that has been severed from its root and has descended into the depths of evil is raised up and restored to its connection through the light of Torah study.
The performance of a commandment draws the vitality concealed within physical things upward and dissolves it into the light of the Ein Sof: Tanya, Part I; Likkutei Amarim 37:5 describes how the energy of the vital animal soul clothed in the limbs that perform a mitzvah rises out of the kelipah and is absorbed into the holiness of the commandment, which is the divine Will itself, and is dissolved into the Ein Sof light — so that the very force of concealment becomes the medium of repair.
The ultimate purpose of tikkun is the transformation of darkness itself into light within this lowest world: Tanya, Part I; Likkutei Amarim 36:5 states that the entire descent of the worlds degree by degree was not for the benefit of the higher worlds — for whom it represents a diminution — but for this lowest world, where the divine Will is that satisfaction be achieved when the sitra achra is subdued and darkness is turned into light, the Ein Sof shining in the very place of the darkness with an intensity greater than its illumination in the higher worlds.
The Ramchal's writings trace tikkun through an eschatological arc culminating in messianic and final rectification: Maamar HaGeulah, Chapter 3 12:2 identifies the repair of the primordial concealment and the blocking of light as the first dimension of tikkun, achieved when the righteous figure descends and empowers the Malkhut to rise from the dust; Maamar HaGeulah, Chapter 7 3:2 envisions the days of Mashiach as the time when the building left incomplete by Adam HaRishon will finally be finished; and Maamar HaGeulah, Chapter 8 12:1 identifies the repair of the body — damaged by Adam's sin and the source of all subsequent corruptions — as the great tikkun of the messianic era, with Maamar HaChochmah, Chelek 1 7:10 adding that the world will be repaired tikkun after tikkun until it is established in the kingdom of God.
The Sefat Emet and the Rav Kook source together open tikkun toward a more encompassing theological dimension: Sefat Emet, Devarim, Nitzavim 5 teaches that God created crooked places even in the supernal worlds that would require rectification through human service — without which the very concept of sin would have no foothold — and that through teshuvah those twisted places are straightened; while Ein Aya, Shabbat 9:45 adds that there is a form of apparent corruption that is in truth itself a great tikkun, recognizable not as a limitation but as a genuine higher wisdom concerning the repair hidden within what only appears to be a defect.
Hasidic sources extend the tikkun framework into practical spiritual repair: Likutei Moharan 29:4 observes that it is impossible to repair each transgression individually in all its particular details, and that there exists instead a comprehensive tikkun — compared to the Brit Kodesh under the name Shadai — that sends light even into the narrow and constricted places no individual repair could reach; and Likutei Moharan 66:1-6 describes the mitigation of anger as a form of tikkun that transforms the smoke of wrath into a tranquil spirit, identifying that purified ruach with the aspect of Mashiach.
The Ramchal's Adir Bamarom grounds the mechanism of tikkun in the structured relationship between the sefirot and their divine root: Adir Bamarom, Beur Idra Rabba 51b explains that Ze'ir Anpin receives its tikkun from Arikh Anpin through the secret of Shabbat — when Ze'ir ascends and Atika is revealed — and that the holiness of Shabbat then sustains even the weekdays; Adir Bamarom, Beur Idra Rabba 22a teaches that for one's tikkunim to be genuinely effective above, one's actions below must be properly ordered in correspondence with the supernal pattern; and Adir Bamarom, Beur Idra Rabba 10b describes how Rashbi sought to bind the ten companions in a strong and complete tikkun — two bonds rather than one — because only a firm and complete binding produces a truly great tikkun above; and Maamar HaGeulah, Chapter 1 3:2 defines the initial act of tikkun as the ordering of spiritual levels in arrangements they did not originally possess, one ordered structure set against each disorder that had arisen.