Luria arrived in Safed around 1570 and died of plague in 1572, aged thirty-eight. His teaching career lasted roughly two to three years, he wrote almost nothing, and he taught orally to a small closed fellowship.
What we have is therefore the work of disciples, above all Hayyim Vital, whose voluminous writings are the principal channel, and the versions disagree. Lawrence Fine's study is the standard account of the circle, its practices, and the transmission problem. Anyone who states the Lurianic system flatly is stating a reconstruction.
The system as it came down reframed Kabbalah around a catastrophe. Tzimtzum: the infinite contracts, withdrawing from a point to make room for anything other than itself, so that creation begins with a divine self-limitation. Shevirat ha-kelim: the vessels made to receive the divine light cannot hold it and shatter, scattering sparks of holiness that fall and become embedded in the shells of the material world. Tikkun: the work of gathering and raising those sparks, which is performed by human beings through observance, intention and prayer.
The reason this spread as no previous Kabbalah had is that it gave a shattered people a cosmology in which their condition was legible. Exile was not merely punishment; exile was the structure of reality, God was in exile too, and the ordinary observant Jew was engaged in repairing the universe. Within a century Lurianic categories were standard across the Jewish world, and they underlie both the Sabbatian movement and Hasidism. Tikkun olam, in its modern and largely secular sense of social repair, descends from Luria by a long and much-altered road.