The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of knowledge that exists on lattice sums and their applications. The authors also provide commentaries on open questions, and explain modern techniques which simplify the task of finding new results in this fascinating and ongoing field. Lattice sums in one, two, three, four and higher dimensions are covered.

When I was a student, in the early fifties, the properties of gratings were generally explained according to the scalar theory of optics. The grating formula (which pre dicts the diffraction angles for a given angle of incidence) was established, exper imentally verified, and intensively used as a source for textbook problems. Indeed those grating properties, we can call optical properties, were taught'in a satisfac tory manner and the students were able to clearly understand the diffraction and dispersion of light by gratings. On the other hand, little was said about the "energy properties," i. e., about the prediction of efficiencies. Of course, the existence of the blaze effect was pointed out, but very frequently nothing else was taught about the efficiency curves. At most a good student had to know that, for an eche lette grating, the efficiency in a given order can approach unity insofar as the diffracted wave vector can be deduced from the incident one by a specular reflexion on the large facet. Actually this rule of thumb was generally sufficient to make good use of the optical gratings available about thirty years ago. Thanks to the spectacular improvements in grating manufacture after the end of the second world war, it became possible to obtain very good gratings with more and more lines per mm. Nowadays, in gratings used in the visible region, a spacing small er than half a micron is common."

This is an advanced text on electromagnetic theory, presenting a systematic discussion of electromagnetic waves and radiation processes in a wide variety of media. The treatment, taken from the field of plasma physics, is based on the dielectric tensor, and this permits the discussion of media outside the scope of the usual approach adopted in most textbooks on electromagnetism. The approach taken also has notable advantages when applied to the conventional emission processes of electromagnetic theory. The authors have thus unified the approaches used in plasma physics and astrophysics on the one hand, and in optics on the other. The book has been written clearly and pedagogically, and will be therefore of value to senior undergraduates, graduate students, lecturers and researchers. Students will find the exercises provided at the end of each chapter particularly useful.

This is an advanced text on electromagnetic theory, presenting a systematic discussion of electromagnetic waves and radiation processes in a wide variety of media. The treatment, taken from the field of plasma physics, is based on the dielectric tensor, and this permits the discussion of media outside the scope of the usual approach adopted in most textbooks on electromagnetism. The approach taken also has notable advantages when applied to the conventional emission processes of electromagnetic theory. The authors have thus unified the approaches used in plasma physics and astrophysics on the one hand, and in optics on the other. The book has been written clearly and pedagogically, and will be therefore of value to senior undergraduates, graduate students, lecturers and researchers. Students will find the exercises provided at the end of each chapter particularly useful.