This text is designed as a basic course in functional analysis for senior undergraduate or beginning postgraduate students. For students completing their final undergraduate year, it is aimed at providing some insight into basic abstract analysis which more than ever, is the contextual language of much modern mathematics. For postgraduate students it is aimed at providing a foundation and stimulus for their further research development.

It is assumed that the student will be familiar with real analysis and have some background in linear algebra and complex analysis. It is also assumed that the student will have studied a course in the analysis of metric spaces such as that given in the author's text

Introduction to the Analysis of Metric Spaces, Cambridge University Press, 1987. Reference to this text will be made under the abbreviation AMS §—.

In AMS, most of the example spaces introduced are normed linear spaces and many of the implications of linear structure were explored. For example when closure in metric spaces was discussed it was natural to consider the closure of linear subspaces in normed linear spaces and when continuity was considered it was logical to study the continuity of linear mappings on normed linear spaces. In order to make this text as self-contained as possible, the example spaces are again introduced and the elementary properties of normed linear spaces are treated but in a more sophisticated way.