Contents 1 Introduction 1 2 Rewrite Systems 7 3 Semigroup Diagrams 9 4 Monoid Pictures 21 5 Diagram Groups 31 6 Squier's Complexes 33 7 Monoid Presentations and The Diagram Groups 39 8 Diagram Groups and Group Theoretic Constructions 45 9 Diagram Groups over Complete Presentations 49 10 Finitely Presented Diagram Groups 57 11 Commutator Subgroups of Diagram Groups 62 12 Asphericity 64 13 Recursive Presentations of Diagram Groups 66 14 Computational Complexity of the Word Problem in Diagram Groups 72 15 Combinatorics on Diagrams 74 16 Different Types of Diagrams and Finitely Presented Simple Groups 97 17 Open Problems 110 vn
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