The Academician I.E. Tamm's disciple, Professor Yu. I Kulakov, when analyzing the structure of physical laws, suggested a theory of physical structures for their classification. Mathematically, a physical structure is a geometry of a special kind. Its metric function assigns a number to a pair of points of two different sets, not one as is the case in conventional geometry. The new geometry, the basics and the results of which this monograph treats, has a group symmetry under Klein and a phenomenological symmetry under Kulakov. The former is determined by a group of motions, and the essence...