Old and new research on the Absolute Parallelism theory

The book shows the sights of Absolute Parallelism (AP), and contains useful information on the problem of singularities, compatibility theory, homotopy groups (also relative and k-ad), topological quasi-charge groups and their morphisms. AP is a single (frame) field theory proposed by Einstein some 80 years ago; it embraces symmetries of both Special and General Relativity. The compatibility theory, if applied to the cases when the frame matrix degenerates, gives a covariant test on singularities of solutions. This gives a single variant (missed in Einstein-Mayer''s list of compatible equations), the unique 5D equation (nothing, nor D, can be changed), which solutions are free of emerging singularities. SO4-symmetrical nonstationary solutions give rise to a cosmological model (relativistic surfing; anti-Milne model in FRW framework) with a specific reduction of the extra-dimension. Topological classification of localized field configurations, combinatorics of topological quasi-charges (quanta), is discussed in an attempt to imagine the Standard Model (and quantum theory itself; and, perhaps, to make some qualitative predictions, like the absence of spin zero elementary quanta).