Metric spaces. Banach and Hilbert Spaces. Linear Operators on Normed Spaces, Bounded and Compact Operators. Spaces of Linear Operators and Convergence. Fundamental Theorems for Normed and Banach Spaces: Hanh-Banach Theorem, Uniform Boundedness Theorem, Open Mapping Theorem, Closed Graph Theorem. Linear Functionals on Hilbert Spaces and Riesz Representation Theorem. Adjoint, Self-adjoint, Unitary and Normal Operators. Spectrum and Resolvent of an Operator. Spectral Properties of Bounded and Compact Operators. Unbounded Operators and Their Basic Properties.

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