The main purpose of this book, based on a course at Universidade Federal do Rio de Janeiro during the summer of 1978, was to provide an introduction to modern infinite dimensional complex analysis, or infinite dimensional holomorphy as it is commonly called, for the graduate student and research mathematician. Since we were more interested in communicating the nature rather than the scope of infinite dimensional complex analysis and since it was clearly impossible to write a comprehensive account of the whole theory for such a short course we were obliged to limit our range and choose to develop a single theme which has made much progress in recent years and which exemplifies the intrinsic nature of the subject, namely the study of locally convex topologies on spaces of holomorphic functions in infinitely many variables.
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