The book begins with the most elementary symmetry concepts, then presents mathematical group theory, and finally the projection operators that flow from the Great Orthogonality are automated and applied to chemical and spectroscopic problems.
From the reviews:
“The layout of McClain’s book definitely reflects the author’s idea of the book, together with multiple examples … . First of all it is partitioned into three Parts which are further spilt into 48 Chapters and three Appendices. … Summarizing, it is likely that tutorial book that many students and PhD students of chemistry, atomic and molecular physics are expected to percept the concept of molecular symmetry practically, interactively via Mathematica with molecules and thus to directly apply them in their own research.” (Eugene Kryachko, Zentralblatt MATH, Vol. 1187, 2010)
W.M. McClain started working with Mathematica as soon as it appeared in 1988, bringing over ten years of nearly daily experience with Mathematica to this book. He has written many research papers that use Mathematica and has also used group theory throughout his 20-year research career in nonlinear spectroscopy. He published the first group theoretic analysis of nonlinear tensors in vibronic sprectroscopy, regarded by many as a landmark paper.