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The book is devoted to a unification of two major principles of invariance in physics (local gauge and local coordinate invariance) and reducing both principles to the second one in a more than 4-dimensional world. The additional dimensions cannot be directly observed. Thus it is akin to a Kaluza-Klein or Jordan-Thiry point of view. The author develops these ideas using nonriemannian geometry from Einstein's Unified Field Theory. The theory uses nonsymmetric right-invariant metric defined on a principal fibre bundle (a gauge bundle). The book proceeds in three stages: "Interference effects" between gravity (described by NGT) and gauge field (including electromagnetic field) which appeared due to nonriemannian geometry in the theory and its physical consequences were discovered. Some applications have been pointed out.