Diagram geometry, which introduces a range of techniques that enable an interaction between group theory and geometry, allows the mathematician to get information on a multi-dimensional geometric object from some knowledge of bi-dimensional properties. This exceptional introduction to the subject provides a wealth of descriptions and examples, explains basic concepts, and details the language of diagram geometrics. It provides an expert development of diagram geometry theory as well as more advanced concepts and techniques. Practical and rigorous, Diagram Geometries is the ideal introduction to the subject for advanced students and researchers in group theory and combinatorics.