Book excerpt: Covering the most important knowledge on optical pumping of atoms, this ready reference is backed by numerous examples of modelling computation for optical pumped systems. The authors show for the first time that modern scientific computing software makes it practical to analyze the full, multilevel system of optically pumped atoms. To make the discussion less abstract, the authors have illustrated key points with sections of MATLAB codes. To make most effective use of contemporary mathematical software, it is especially useful to analyze optical pumping situations in the Liouville space of density matrices rather than in the traditional Hilbert space of wave functions. This unique approach allows modelling under most experimental conditions, e.g. - magnetic resonance with one or more oscillating magnetic fields, - coherent population trapping or CPG resonances induce by modulated light, - magneto-optic forces on multilevel atoms, - various spin-relaxation processes etc. The reader of this book should have a basic understanding of quantum mechanics, atomic physics, optics and magnetic resonance. Some familiarity with MATLAB would be helpful to a reader interested in writing specialized programs based on the illustrative codes to analyze specialized optical-pumping phenomena.