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This is original, well-written work of interest

Presents for the first time (physical) field theories written in sheaf-theoretic language

Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments

Author's mastery of the subject and the rigorous treatment of this text make it invaluable

Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate...