This ready reference covers the most important facts about optical pumping and spin relaxation of atoms. The authors show that systematic use of Liouville space together with modern scientific computing software makes it practical to analyze the full, multilevel system of optically pumped atoms. Sections of MATLAB codes included in the text allow the reader to assemble quite sophisticated codes for modelling various optical-pumping phenomena. The text assumes that the reader has a basic understanding of quantum mechanics, atomic physics, optics, magnetic resonance, and the mathematics of physics and chemistry.