“The art of doing mathematics,” Hilbert has said, “consists in finding that special case which contains all the germs of generality.” In our view, angular momentum theory plays the role of that “special case,” with symmetry—one of the most fruitful themes of modern mathematics and physics—as the “generality.” We would only amend Hilbert's phrase to include physics as well as mathematics. In the Preface to the second edition of his famous book Group Theory and its Applications to the quantum Mechanics of Atomic Spectra, Wigner records von Laue's view of how remarkable it is that “almost all the rules of [atomic] spectroscopy follow from the symmetry of the problem.” The symmetry at issue is rotational symmetry, and the spectroscopic rules are those implied by angular momentum conservation. In this monograph, we have tried to expand on these themes.

The fact that this monograph is part of an encyclopedia imposes a responsibility that we have tried to take seriously. This responsibility is rather like that of a library. It has been said that a library must satisfy two disparate needs: One should find the book one is looking for, but one should also find books that one had no idea existed. We believe that much the same sort of thing is true of an encyclopedia, and we would be disappointed if the reader did not have both needs met in the present work.