Normed linear spaces, Banach spaces, Classical examples: C[0,1], lp, C, C0, C00, Lp[0,1], Continuity of Linear Operator and bounded linear operator, Quotient spaces 

Finite dimensional normed spaces, Riesz lemma, (non) compactness of unit ball, Hahn Banach theorem and Its consequences. 

Uniform Boundedness principle, Closed Graph Theorem, Bounded Inverse Theorem, Open Mapping Theorem, Banach Steinhauss Theorem 

Bounded Linear Functionals, Dual space of classical spaces, Reflexivity of the Banach Space, Hilbert spaces, Projection theorem, Orthonormal basis, Bessel inequality, Parseval’s equality Seperable Hilbert spaces and Countable orthonormal basis, example of non seperable spaces, Uncountable orthonormal basis and definition of convergence of Fourier series – Riesz-Fisher‘s theorem, Riesz representation theorem 

1. Linear Analysis by Bela Bollobas, Cambridge University Press, 1999 
2. Functional Analysis by Balmohan V Limaye, New Age International Publishers, Third Ed, Reprint2014.
3. Introduction to Topology and Modern Analysis by G. F. Simmons, McGraw Hill Education, 2004 
4. Thamban Nair, Functional Analysis: A First Course, PHI, 2001.