Kapitel 1. Metric and normed spaces
 Metric spaces
 Normed spaces
 Examples
 Compactness
 Cardinality of Sets
 The StoneWeierstraß theorem
 Banach‘s fixed point theorem
 Lp spaces
 Equivalent norms
 Compactness in normed spaces
Kapitel 2. Linear and continuous operators
 Basics
 Examples
Kapitel 3. Main Theorems about Operators
 Baire‘s theorem
 Uniform boundedness principle
 Open mapping theorem
 Continuous inverse theorem
 Closed Graph theorem
Kapitel 4. Hilbert spaces
 PreHilbert spaces
 Hilbert spaces and normed spaces
 Best approximation
 Projection theorem
 FréchetRiesz representation theorem
 Orthonormal systems and bases in Hilbert spaces
 FischerRiesz theorem
 The spectral theorem for compact selfadjoint operators
Kapitel 5. Dual spaces
 Examples
 The HahnBanach theorem and its consequences
Kapitel 6. Spectrum of compact operators – Fredholm theory
 Adjoint operators
 The spectrum of bounded operators
 Fredholm theory
