This is the first of a five-volume exposition of the main principles of nonlinear functional analysis and
its applications to the natural sciences, economics, and numerical analysis. The presentation is self-contained and
accessible to the nonspecialist. Among the topics of Volume I are the two basic fixed-point theorems of Banach and
Schauder, calculus in Banach spaces, the implicit function theorem, Newton`s method, analytic bifurcation theory,
fixed-point theorems for multivalued mappings, nonexpansive and condensing operators, mapping degree and fixed-point
index and their applications, analytic maps, and asymptotic fixed-point theorems.
The book contains numerous applications to such areas as ordinary and partial differential equations,
integral equations, and game theory. Many exercises and a comprehensive bibliography complement the text.