Unit I: Normed linear space; Banach spaces and basic properties; Heine-Borel theorem, Riesz lemma and best approximation property; Inner product space and projection thoerem; Orthonormal bases; Bessel inequality and Parseval's formula; Riesz-Fischer theorem. Unit II: Bounded operators and basic properties; Space of bounded operators and dual space; Riesz representation theorem; Adjoint of operators on a Hilbert space; Examples of unbounded operators; Convergence of sequence of operators. Unit