Thesis (M.S., Chemistry) -- University of Idaho, 2017 | Several textbooks on chemical group theory were examined and showed a wide range of inconsistencies in content. Many authors attempt to make their texts student-friendly by stripping out linear algebra concepts and focusing instead on visualizations of symmetry operations. This inevitably leads to an incomplete understanding of how to apply group theory to chemistry, and the lack of a standard across texts can lead a student who is using multiple sources to come to an incorrect conclusion. A guide was crafted to provide continuity across previously published group theory texts and to fill in the missing linear algebra concepts. It contains explanations of how to derive the rotation matrices for both clockwise and anticlockwise rotation, as well as reflection, inversion, and improper rotation. In addition, the guide shows how to derive a character table and includes the matrices for symmetry operations organized by principal rotation axis.