The author describes the current state of the art in the theory of
invariant random fields. This theory is based on several different areas
of mathematics, including probability theory, differential geometry,
harmonic analysis, and special functions. The present volume unifies
many results scattered throughout the mathematical, physical, and
engineering literature, as well as it introduces new results from this
area first proved by the author. The book also presents many practical
applications, in particular in such highly interesting areas as
approximation theory, cosmology and earthquake engineering. It is
intended for researchers and specialists working in the fields of
stochastic processes, statistics, functional analysis, astronomy, and
engineering.