This is a collection of 26 “reprints” on diffraction, defined by the editors as “the response of waves to local heterogeneity in the medium in which they propagate.” Actually, the word “reprint” may be misleading: every article has been retyped into two-column format, and a few articles are translations into English. It is unclear how the editors guarded against introducing new errors, or if they corrected known errors.

The collection is divided into four chapters and two appendixes. Chapter 1 (Overview, six articles) is mainly concerned with Keller's Geometrical Theory of Diffraction (GTD) together with its context. It includes Keller's first announcement of GTD in the proceedings of a 1953 conference, his 1977 Gibbs lecture and, in Chap. 4, his well-known 1962 paper on GTD and his 1960 paper with Buchal on boundary-layer problems. Chapter 1 also includes Bouwkamp's famous 1954 survey article, a new translation of a 1913 paper by Arkadiew on diffraction phenomena, a nice historical article by Malyuzhinets from 1959, and a 1995 paper by Ufimtsev on the contributions of Rubinowicz.

Chapter 2 (Early Developments in Diffraction Theory, 3 articles) starts with a 17-page introduction by the editors, “outlin[ing] the historic development of diffraction theory from Grimaldi to Young, [beginning] with a brief history of early optics prior to the discovery of diffraction by Grimaldi in 1665. Major contributions follow, including those by Huygens (1678) and Young (1803).” There is a new translation of some of Grimaldi's writings (from Latin into English via German), an old translation of a piece of Huygens' *Treatise on Light*, and Young's Royal Society paper in which he describes his experiments proving the wave-like nature of light.

Chapter 3 (The Classical Mathematical Theory of Diffraction, five articles) also starts with a substantial introduction by the editors. The five articles are all from the 19th century and they are by men with familiar names: Fresnel, Green, Helmholtz, Kirchhoff, and Rayleigh. In particular, there is a new translation of part of an 1859 paper by Helmholtz in which he derives an integral representation for solutions of the Helmholtz equation inside a bounded three-dimensional region using cos(*kr*)/*r* as what we would call a Green's function. There is also a new translation of Kirchhoff's 1882 paper, the one containing his derivation of an integral representation for time-dependent, transient acoustic fields. This paper also contains Kirchhoff's inconsistent approximation for scattering by an aperture in a screen, obtained by specifying both the field and its normal derivative on the screen. [For a recent analysis, see J. Z. Buchwald and C.-P. Yeang, Kirchhoff's theory for optical diffraction, its predecessor and subsequent development: the resilience of an inconsistent theory, *Archive for History of Exact Sciences*, Vol. 70, pp. 463–511 (2016).] Rayleigh's 1897 paper in the collection gives his (consistent) low-frequency approximations for “the passage of waves through” small apertures in plane screens.

Chapter 3 also has two appendixes, one on the “Cornu spiral” (Cornu, 1874) and one on “Babinet's principle” (Babinet, 1837); both are new translations of the original papers.

Chapter 4 (Foundations of Modern Diffraction Theory, eight articles) contains papers from the 20th century. The editors attempt to “cover the step changes that distinguish modern diffraction theory from classical theory. …The general trend …is characterized by attempts to overcome the limitations [im]posed by the Kirchhoff approximation, introduction of the geometrical theory of diffractions, and extension of the scalar diffraction problem of optics to the vector problem for electromagnetic waves.” Prior to Keller's two GTD papers mentioned above, there is a pair of papers from 1922 by Coulson and Becknell and a paper by Van Kampen from 1949. These are followed by a well-known 1974 paper on uniform GTD by Kouyoumjian and Pathak and a paper by Klem-Musatov and Aizenberg (1984) with more emphasis on elastic waves. (Four of the papers from Chap. 4 can be found in *Selected Papers on Geometrical Aspects of Scattering* (P. L. Marston, ed.), Vol. MS89, SPIE Press, Bellingham, WA, 1994.) The last paper in Chap. 4 is an outlier. It is a 1997 “tutorial paper” by Bertero, Boccacci, and Piana entitled “Resolution and super-resolution in inverse diffraction”; it is an interesting article but it does not fit into the collection as a whole.

Some readers of the *Journal of the Acoustical Society of America* may also be interested in the companion collection on *Seismic Diffraction* (SEG Geophysics Reprint Series No. 30, 2016) and the earlier *Classics of Elastic Wave Theory* (SEG Geophysics Reprint Series No. 24, 2007).