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We have considered writing the present book for a long time, since the lack of a sufficiently complete textbook about complex analysis in infinite dimensional spaces was apparent. There are, however, some separate topics on this subject covered in the mathematical literature. For instance, the elementary theory of holomorphic vector- functions.and mappings on Banach spaces is presented in the monographs of E. Hille and R. Phillips 1] and L. Schwartz 1], whereas some results on Banach algebras of holomorphic functions and holomorphic operator-functions are discussed in the books of W. Rudin ...

Bridges the gap between nonlinear analysis, nonlinear operator equations and the theory of holomorphic mappings on Banach spaces. This book concludes with a brief exposition of the theory of spaces with indefinite metrics, and some relevant applications of the holomorphic mappings theory in this setting.