Specific knowledge about the society is scarce. The Order of the Illuminati was established with some unspecified ties to the Masonic lodges of Germany; as a secret society within a secret society, the Illuminati have produced at least as many myths as verifiable facts. The sympathies and beliefes of Weishaupt himself, for instance, have been claimed by countless groups -- atheists, Cabalists, rationalists, democrats, socialists, anarchists. Some trace the Illuminati back to the Knights Templar, to Gnostic cults, to ancient Egypt, and even to Atlantis. In the 1790s, some credited (or blamed) the society with manipulating the American and French Revolutions. In the United States, Federalists encouraged people to believe Thomas Jefferson and the Democratic Republican Party were controlled by the Illuminati in Europe.
It is not strictly necessary to disentangle fact from fiction, since the influence of the Order was greater in legend than in fact. But several things can be stated about the Illuminati with some degree of certainty. The two central figures in the organization were Weishaupt and Adolph Franz Friedrich Ludwid Baron Von Knigge. The members of the Illuminati are known to have favored free-thinking and radical politics, and were often alleged to have ties with Jacobins (Weishaupt and the Illuminati are discussed in Abbé Barruel's History of Jacobinism, which Mary Shelley is known to have read in October 1814). The Order promoted a belief in deism and a doctrine of spiritual perfection: the society was in fact first known as the Order of Perfectibilists.
At their height, the Illuminati claimed over two thousand members, not only in Germany but in France, Belgium, Holland, Denmark, Sweden, Poland, Hungary, and Italy, including Goethe, Herder, and many other prominent nobles and reformers. But the Bavarian government cracked down on the Illuminati and other secret societies in 1784 for allegedly plotting a massive overthrow of Europe's monarchies, although it was unable to squelch them entirely. By the end of the eighteenth century, however, the Illuminati had effectively disbanded, although legends of their continued existence (and influence) persist into the twentieth century (among, for instance, members of the John Birch Society). Perhaps some of this confusion is owing to the fact that over time, the word illuminati came to be used more expansively for many enthusiasts of Enlightenment, including the followers of Emmanuel Swedenborg.