From the reviews: "This is a very nice book for those interested in the theory of diffraction since it presents, for the first time in English, the strikingly original work of Sommerfeld-which marks a milestone in optical theory-enriched with historical background and technical details. The interest of this book is not only historical but also technical as it presents a surprisingly rich and complex mix of pure and applied mathematics."(MATHEMATICAL REVIEWS) "This book offers the first publication in English of Sommerfeld's original work, together with extensive notes by the translators, and it can be recommended to anyone interested in the theory of diffraction. ... The translator's notes (64 pages) are very illuminating for the reader by providing a lot of historical remarks, technical details, and a nice account of previous diffraction analyses of Kirchhoff and Poincare." (Johannes Elschner, Zentralblatt MATH, Vol. 1109 (11), 2007)

• 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.

From the reviews: "This is a very nice book for those interested in the theory of diffraction since it presents, for the first time in English, the strikingly original work of Sommerfeld-which marks a milestone in optical theory-enriched with historical background and technical details. The interest of this book is not only historical but also technical as it presents a surprisingly rich and complex mix of pure and applied mathematics."(MATHEMATICAL REVIEWS) "This book offers the first publication in English of Sommerfeld's original work, together with extensive notes by the translators, and it can be recommended to anyone interested in the theory of diffraction. ... The translator's notes (64 pages) are very illuminating for the reader by providing a lot of historical remarks, technical details, and a nice account of previous diffraction analyses of Kirchhoff and Poincare." (Johannes Elschner, Zentralblatt MATH, Vol. 1109 (11), 2007)

• 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.