The Rosicrucians are an occult sect originating in either the 15th or 17th century, depending on which account you accept. The latter is the more plausible and involves the 1610 publication by Johann Valentine Andrea of a work called Fama Fraternitatis, which purported to be a history of a society of mystical healers begun by the German scholar Christian Rosenkreuz. Though this "history" was later admitted to be a complete fabrication, the concept of a brotherhood of men interested in science, medicine, and occultism was a fashionable one at the time and took root in Germany; the Brotherhood of the Rosy Cross spread also to England.
The history of this movement becomes vague after the end of the 17th century, and little is known of it until 1866, when modern Rosicrucianism was organized as a branch of Freemasonry. It spread from England to the United States and then back to Continental Europe, and by the end of the 19th century, Rosicrucians had established numerous lodges, colleges, and regional headquarters throughout the Western world.
Rosicrucian theology is vague and undefined. It has borrowed certain Christian concepts while rejecting others, viewing "all things as complicitly and ideally in God" and tending toward a kind of pantheism. Here there are similarities (unsurprisingly) with the occultic religion of upper-level Freemasonry. Despite their name, the Rosicrucians are not a Christian denomination, nor even a quasi-Christian sect; a Catholic should have nothing to do with them.