discoveries within the literature and lends itself to alternative descriptions of certain preexisting results and problems. Each chapter contains an outline of its structure. Chapter 5 and part of Chapter 6 form the bulk of [2]; Chapter 2 together with the remainder of Chapter 6 will appear as [1]; Chapter 3 will be availabe as [3]. Chapter 1 establishes the necessary definitions and notation. After defining singular Artin monoids (SGM), their “counter-parts”, positive singular Artin monoids (SG + ), and their various types, we expound their place in the literature. More specifically, we discuss their relationship with other classes of monoids (which include Garside and chainable) and groups (Garside, Coxeter and Artin). We also state certain known facts and problems pertinent to the thesis. In Chapter 2, we address the issue of divisibility in positive singular Artin monoids and review the relevant literature. The deductions we obtain are interesting in their own right, but they also have strong import in subsequent chapters. Chapter 3 is devoted to showing that any SG + naturally embeds into SGM. In Chapter 4, the desingularisation map ( ) is defined, and (a generalised form of) “Birman’s conjecture” is stated; namely, that injects from any singular Artin monoid into its corresponding group algebra. This is followed by a history of the discoveries regarding the conjecture. The inferences of Chapters 2 and 3 are then invoked to immediately acquire new results regarding the faithfulness of . In order to further investigate the aforementioned conjecture, a positive form is required. Chapter 5 sets up the requisite “machinery”, and in Chapter 6 we infer that the restriction of to certain submonoids of SGM is faithful, expanding on the deductions