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 of the latter is in the existence of some dependence among all the values of a metric function for any subsets of a certain number of points from each set. Both symmetries turn out to be equivalent. Quasigroups with a right one and hyper-complex numbers reveal themselves with precision up to isotopy in the structure of the metric function giving a geometry of two sets and in the equation that...

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