Descriptions of the inhomogeneity including dislocations and defects based on the differential geometry forms the basic core of FTMP. This chapter first provides the basic notions of differential geometry necessary for understanding “non-Riemannian plasticity.” The fundamental concepts and quantities are presented second, which is followed by some new features peculiar to the present field theory of multiscale plasticity.

This chapter intends to overview the field theory of multiscale plasticity (FTMP) in terms of the key concepts (keywords), the basic theories, and the fundamental hierarchical recognition (i.e., the identification of important scales). This will be followed by the introductions of several new features that the author himself has found and introduced afresh. Practically, the theory is applied via the crystal plasticity formalism-based framework as a tentative and convenient vehicle. So, the constitutive framework together with some detailed sets of modeling for the evolution equations therein is are also presented in the present chapter, i.e., strain gradient terms for the dislocation-density and the incompatibility tensors.