For closed manifolds, there is a highly elaborated theory of
number-valued invariants, attached to the underlying manifold,
structures and differential operators. On open manifolds, nearly
all of this fails, with the exception of some special classes. The
goal of this monograph is to establish for open manifolds,
structures and differential operators an applicable theory of
number-valued relative invariants. This is of great use in the
theory of moduli spaces for nonlinear partial differential
equations and mathematical physics. The book is self-contained: in
particular, it contains an outline of the necessary tools from
nonlinear Sobolev analysis.
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