This monograph is concerned with the fundamentals of up-to-date geo-
metrical optics treated as an approximate method of wave theory.
Geometrical optics has changed dramatically over the last two decades.
Primarily, it has acquired a number of novel disciplines: space-time
geo- metrical optics, the quasi-isotropic approximation, the modern
theory of caustics related to catastrophe theory, and perturbation
techniques for rays, to name only a few. Another acquisition is the
reliable boundaries of appli- cability for geometrical optics, based
upon the concept of the Fresnel volume for a ray. These recent additions
to the field are the focus of dis- cussion in the book. We did not
attempt to separate study-oriented and illustrative material from that
intended for professionals, but rather we spread it throughout the text
to facilitate for the reader the mastering of this attractive,
intuitively appealing and efficient ray method. In preparing the
manuscript we used a set of lecture notes devised for All-Union Schools
on Diffraction and Wave Propagation, published in Rus- sian. Sections
2.1-4,6 and 10 result from joint efforts of both authors. The other
material of the book we wrote separately. I contributed Sects. 2.5,9 and
3.17 and Chap.4; Yu.l. Orlov prepared the rest. Unfortunately, he could
not take part in the preparation of the English edition, as he died in
1982 at the age of 41, on the verge of what would have been great
achieve- ments considering his strong and original talent.