This text, in a sense, continues the treatment of the earlier Volume 6 in the "Springer Series on Wave Phenomena", titled "Geometrical Optics of Inhomogenous Media", by analyzing caustics and their fields on the basis of modern catastrophe theory. This volume covers the key generalizations of geometrical optics related to caustic asymptotic expansions: The Lewis-Kravtsov method of standard functions; Maslov's method of canoncial operators; Orlov's method of interference integrals, as well as their modifications for penumbra, space-time, random and other types of caustics. All the methods are illustrated by worked problems concerning relevant wave-field applications.
Rays and caustics; caustics as catastrophes; typical integrals of catastrophy theory; uniform caustic asymptotics; derived with standard integrals; Maslov's method of the canonical operator; method of interference integrals; penumbra caustics; modifications and generalizations of standard integrals and functions; caustics revisited.
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