Mathematical Theory of Diffraction.- 1. General problem formulation.- 2. Expansions in Bessel functions.- 3. Transition from ?u = 0 to ?u + k2u = 0.- 4. Bessel functions as the simplest examples.- 5. Everywhere finite solutions.- 6. Solutions with a singularity.- 7. Graphical treatment of the simplest multivalued solution.- 8. Application to diffraction.- Tafel.- Translators' Notes.- References.- Appendix I: The History and Present State of Discoveries relating to Vision, Light and Colours.- Appendix II: On the Mathematical Theory of Diffraction Phenomena.

A. Sommerfeld's "Mathematische Theorie der Diffraction" marks a milestone in optical theory, full of insights that are still relevant today. In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffraction analysis is a surprisingly rich and complex mix of pure and applied mathematics, and his often-cited diffraction solution is presented only as an application of a much more general set of mathematical results. This complete translation, reflecting substantial scholarship, is the first publication in English of Sommerfeld's original work. The extensive notes by the translators are rich in historical background and provide many technical details for the reader.