Metric Spaces. Normed Spaces; Banach Spaces. Inner Product Spaces; Hilbert Spaces. Fundamental Theorems for Normed and Banach Spaces. Further Applications: Banach Fixed Point Theorem. Spectral Theory of Linear Operators in Normed Spaces. Compact Linear Operators on Normed Spaces and Their Spectrum. Spectral Theory of Bounded Self-Adjoint Linear Operators. Unbounded Linear Operators in Hilbert Space. Unbounded Linear Operators in Quantum Mechanics. Appendices. References. Index.