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A First Course in Functional Analysis lucidly covers Banach spaces, continuous linear functionals, the basic theorems of bounded linear operators, Hilbert spaces, operators on Hilbert spaces, spectral theory and Banach algebras usually taught as a core course to post-graduate students in mathematics. The special distinguishing features of the book includes the establishment of the spectral theorem for the compact normal operators in the infinite dimensional case exactly in the same form as in the finite dimensional case and a detailed treatment of the theory of Banach algebras leading to the proof of the Gelfond – Neumark structure theorem for Banach algebras. Key Features Examples at the End of Each Chapter Elementary Problems to Illustrate Theory Challenging Exercises as Theorems. Table of Contents Preface Banach Spaces Continuous Linear Functionals The Basic Theorems of Bounded Linear Operators Hilbert Spaces Operators on Hilbert Spaces Spectral Theory Banach Algebras References Index.