This text details the symmetry groups within electromagnetism and Unified Field Theory. It explains many common symmetry groups and linear and rotational transformations from a quantum perspective, and contextually relates them to electromagnetism. Of particular interest is the information on the Lorentz group and its transformation and mapping as well as classifying the conjugacy classes with unitary symmetry and quark states. Offering a fresh perspective to both quantum physics and electromagnetism, this book will appeal to both physicists and mathematicians alike, since it offers many new insights into the question of symmetry of the quantum state as it relates to electromagnetism.