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 fields and general relativity. These texts contains a
treasure trove of minutely detailed and rigorous computations. This
original work will appeal to advanced undergraduates, graduate students,
mathematicians and physicists interested in applications of differential
geometry to physical theories.