This is the author's abstract of his doctoral dissertation, submitted as part of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics at Duke University. In it, he explores the classic problem in permutation theory based on the Riffle Shuffle and Cut. The Faro Shuffle and the permutations related to the Out Faro and the In Faro are fully defined in theorem. In addition to the Faro Shuffle, he explores Q-Dimensional Decks and includes references for his work. Because this is not a book of general interest to magicians, only a limited number have been printed.