Normed spaces, Banach spaces, properties of normed spaces, Compactness and finite dimension, Bounded and continuous linear operators, Hahn-Banach theorem and its applications, Open mapping and closed graph Theorem, Representation of Dual spaces , Bounded and Copmpact Operator, Adjoint operators, Spectrum and Gelfund- Mazur Theorem. Weak Topology and Banach-Alaoglu Theorem, Reflexiv spaces.

Inner product spaces, Hilbert spaces, Representation of functionals on Hilbert spaces, Adjoint operator, Self-adjoint, unitary operators, Spectrum.

B. V. Limaye, Functional Analysis, New Age International, 1996.

Y. Eidelman, V. D. Milman, A. Tsolomitis, Functional Analysis: An Introduction, AMS Bookstore, 2004.

E. Kreyszig, , Introductory Functional Analysis with Applications, Wiley, 1978