  The theory of Physical Structures (TPS) was put forward by Professor Yu.I.
Kulakov for the sake of classifying the laws of Physics. The history of the
development of that theory is given in his monograph [1]. A physical structure
is a geometry of one or two sets whose metric function assigns a number to
every pair of points. Its phenomenological symmetry, under Kulakov, means that
for every collection of some finite number of points all of their reciprocal
distances are functionally related. Such geometries are endowed with a group
symmetry under Klein, which is equivalent to the phenomenological symmetry, and
many of them have an essential physical interpretation. That is why they are to
be defined precisely and explored as purely mathematical objects. In this
monograph we treat the mathematical basics of the TPS and present the results
of attempts at classification that have been obtained by now. We hope that the
monograph will be of interest for research workers and teachers, senior and
post graduate students, as well as to all those interested in algebra, geometry
and theoretical physics who would like to use the TPS in their research
projects or could want to contribute to the development of its mathematical
apparatus.
