During the last few decades, the subject of potential theory has not
been overly popular in the mathematics community. Neglected in favor of
more abstract theories, it has been taught primarily where instructors
have ac- tively engaged in research in this field. This situation has
resulted in a scarcity of English language books of standard shape,
size, and quality covering potential theory. The current book attempts
to fill that gap in the literature. Since the rapid development of
high-speed computers, the remarkable progress in highly advanced
electronic measurement concepts, and, most of all, the significant
impact of satellite technology, the flame of interest in potential
theory has burned much brighter. The realization that more and more
details of potential functions are adequately visualized by "zooming-
in" procedures of modern approximation theory has added powerful fuel to
the flame. It seems as if, all of a sudden, harmonic kernel functions
such as splines and/or wavelets provide the impetus to offer appropriate
means of assimilating and assessing the readily increasing flow of
potential data, reducing it to comprehensible form, and providing an
objective basis for scientific interpretation, classification, testing
of concepts, and solutions of problems involving the Laplace operator.