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This text is a basic course in functional analysis for senior undergraduate and beginning postgraduate students. It aims at providing some insight into basic abstract analysis which is now the contextual language of much modern mathematics. Although it is assumed that the student will have familiarity with elementary real and complex analysis and linear algebra and have studied a course in the analysis of metric spaces, a knowledge of integration theory or general topology is not required. The theme of this text concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. But the implications of the general theory are illustrated with a great variety of example spaces.

Normed linear spaces. --- Mathematical analysis.

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Espaces linéaires normés. --- Normed linear spaces

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Metric spaces. --- Normed linear spaces. --- Functional analysis.

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This work provides a comprehensive overview of the characterizations of real normed spaces as inner product spaces based on norm derivatives and generalizations of the most basic geometrical properties of triangles in normed spaces.

Normed linear spaces. --- Inner product spaces.

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Normed linear spaces. --- Espaces linéaires normés. --- Espaces de banach