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This book has its origin in lectures given at the Tata Institute of Fundamental Research, Bombay in the winter of 1964/65. The aim of the lectures was to present various topics in analysis, both on real and on complex manifolds. It is unnecessary to add that the topics actually chosen were determined entirely by personal taste. The contents were issued as lecture notes by the Tata Institute, and the present book is based on these notes.

The book is meant for people interested in analysis, who have little analytical background. The elements of the theory of functions of real variables (differential and integral calculus and measure theory) and some complex variable theory are assumed. Elementary properties of functions of several complex variables which are used are, in general, stated explicitly with references. It is however supposed that the reader is well acquainted with linear and multilinear algebra (properties of duals, tensor products, exterior products and so on of vector spaces) as well as set topology (properties of connected and

locally compact spaces).

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