1. The origin of the quantum theory Planck's radiation formula 2. The nuclear theory of the atom Bohr's theory of the hydrogen spectrum 3. The correspondence principle the photo-electric effect Einstein's deduction of Planck's formula 4. The adiabatic principle of Ehrenfest the stationary states of a periodic system 5. General dynamical theory 6. Contact transformations the Hamilton-Jacobi differential equation 7. The use of angle variables multiply periodic systems 8. The relativity theory of the fine structure of the hydrogen lines electron in a central field 9. The Stark effect 10. The Zeeman effect 11. The series spectra of the elements 12. The multiple structure of series lines theory of the Ritz formula 13. Arc and spark spectra excitation of lines by electrons or radiation 14. X-ray spectra 15. Absorption spectra and absorption edges Bohr's table of the atomic structures of the elements 17. Band spectra in the infra-red 18. Band spectra in the optical region molecular rotation and specific heat 19. The Keplerian orbit the Delaunay elements 20. The astronomical theory of perturbations and atom mechanics 21. General perturbation theory 22. The effect of electric and magnetic fields on the spectra of elements of higher atomic number. Recent developments of the quantum theory: the doublet theories of Sommerfield and Lande the dispersion theory of Kramers the quantum-kinematics of Heisenberg Index of authors.