This 2-volume research monograph presents a new kind of modern
differential geometry approach to such physical theories as gauge
theory. Sheaf theory (geometry) and sheaf cohomology (analysis) are used
to explain all the machinary of classical differential geometry without
any notion of smoothness. Together they present Maxwell fields,
Yang-Mills and general relativity. The text contains a treasure trove of
minutely detailed and rigorous computations. This original work will
appeal to physicists, mathematicians, graduate and advanced
undergraduate students studying applications of differential geometry
tor physical theories.