The paper gives an account of the author's work on a new form of quantum theory. \textsection{}1. The Hamiltonian analogy between mechanics and optics. \textsection{}2. The analogy is to be extended to include real "physical" or "undulatory" mechanics instead of mere geometrical mechanics. \textsection{}3. The significance of wave-length; macro-mechanical and micro-mechanical problems. \textsection{}4. The wave-equation and its application to the hydrogen atom. \textsection{}5. The intrinsic reason for the appearance of discrete characteristic frequencies. \textsection{}6. Other problems; intensity of emitted light. \textsection{}7. The wave-equation derived from a Hamiltonian variation-principle; generalization to an arbitrary conservative system. \textsection{}8. The wave-function physically means and determines a continuous distribution of electricity in space, the fluctuations of which determine the radiation by the laws of ordinary electrodynamics. \textsection{}9. Non-conservative systems. Theory of dispersion and scattering and of the "transitions" between the "stationary states." \textsection{}10. The question of relativity and the action of a magnetic field. Incompleteness of that part of the theory.