Introduction to Functional Analysis with Applications

1. Metric Spaces
2. Normed Spaces. Banach Spaces
3. Inner Product Spaces. Hilbert Spaces
4. Fundamental Theorems for Normed and Banach Spaces
5. Further Applications: Banach Fixed Point Theorem
6. Further Applications: Approximation Theory
7. Spectral Theory of Linear Operators in Normed Spaces
8. Compact Linear Operators on Normed Spaces and Their Spectrum
9. Spectral Theory of Bounded Self-Adjoint Linear Operators
10. Unbounded Linear Operators in Hilbert Space
11. Unbounded Linear Operators in Quantum Mechanics