Part 1 - Introduction and Metric Space
Part 2 - Examples for Metrics
Part 3 - Open and Closed Sets
Part 4 - Sequences, Limits and Closed Sets
Part 5 - Cauchy Sequences and Complete Metric Spaces
Part 6 - Norms and Banach Spaces
Part 7 - Examples of Banach Spaces
Part 8 - Inner Products and Hilbert Spaces
Part 9 - Examples of Inner Products and Hilbert Spaces
Part 10 - Cauchy-Schwarz Inequality
Part 11 - Orthogonality
Part 12 - Continuity
Part 13 - Bounded Operators
Part 14 - Example Operator Norm
Part 15 - Riesz Representation Theorem
Part 16 - Compact Sets
Part 17 - Arzelà–Ascoli Theorem
Part 18 - Compact Operators
Part 19 - Hölder’s Inequality
Part 20 - Minkowski Inequality
Part 21 - Isomorphisms?
Part 22 - Dual Spaces
Part 23 - Dual Space - Example
Part 24 - Uniform Boundedness Principle / Banach–Steinhaus Theorem
Part 25 - Hahn–Banach Theorem
Part 26 - Open Mapping Theorem
Part 27 - Bounded Inverse Theorem and Example
Part 28 - Spectrum of Bounded Operators
Part 29 - Spectrum of Multiplication Operator
Part 30 - Properties of the Spectrum
Part 31 - Spectral Radius
Part 32 - Normal and Self-Adjoint Operators
Part 33 - Spectrum of Compact Operators
Part 34 - Spectral Theorem for Compact Operators