Preface.- Introduction.- Mathematical Theory of Diffraction.- General problem formulation.- Expansions in Bessel functions.- Transition formula.- Bessel functions as the simplest examples.- Everywhere finite solutions.- Solutions with a singularity.- Graphical treatment of the simplest multivalued solution.- Application to diffraction.- Tafel.- Translators' Notes.- Appendix I: The History and Present State of Discoveries relating to Vision, Light and Colours, Joseph Priestley, London, 1772, pp. 171-182.- Index.