  Weyl’s book (Weyl (1931b, 2 edn)) is remarkably complete for such an  early work and covers many topics. Chapters I and III are mainly  concerned with preliminary mathematical concepts. The first chapter  provides an account of the theory of finite dimensional Hilbert  spaces and the third chapter is an exposition of the unitary  representation theory of finite groups and compact Lie groups.  Chapter II is entitled Quantum Theory; it is the earliest  systematic and comprehensive account of the new quantum theory.  Chapter IV, entitled Application of the Theory of Groups to Quantum Mechanics, is divided into four parts. In part A,  entitled The Rotation Group, Weyl provides a systematic  explanatory account of the theory of atomic spectra in terms of the  unitary representation theory of the rotation group, followed by a  discussion of the selection and intensity rules. Part B is entitled  The Lorentz Group. After discussing the spin of the electron and its role in accounting for the anomalous Zeeman effect, Weyl  presents Dirac’s theory of the relativistic quantum mechanics of the  electron and develops in detail the theory of an electron in a  spherically symmetric field, including an analysis of the fine  structure of the spectrum. In part C, entitled The Permutation  Group, Weyl applies the Pauli exclusion principle to explicate  the periodic table of the elements. Next, Weyl develops the second  quantization of the Maxwell and Dirac fields required for the  analysis of many body relativistic systems. Weyl noted in the preface to the second edition that his treatment is in accordance with the  recent work of Heisenberg and Pauli. It is now customary to include  such a topic under the heading of relativistic quantum field theory.  The final part of Chapter IV, part D, is entitled Quantum Kinematics; it provides an exposition of part II of Weyl’s  (1927) paper, mentioned earlier. Chapter V, entitled The  Symmetric Permutation Group and the Algebra of Symmetric  Transformations, is for the most part pure mathematics. It is  widely regraded to be the most difficult part of the Weyl’s book. 