目次

1 Introduction and Mathematical Backgrounds.- 2 Normed and Banach Spaces, Examples and Applications.- 3 Hilbert Spaces and Bounded Operators.- 4 Families of Compact Operators on Hilbert Spaces and Fundamental Properties.- 5 Densely-Defined Unbounded Operators on Hilbert Spaces.- 6 Phenomenology of Quantum Systems and Wave Mechanics: an Overview.- 7 The First 4 Axioms of QM: Propositions, Quantum States and Observables.- 8 Spectral Theory I: Generalities, Abstract C -algebras and Operators in B(H).- 9 Spectral theory II: Unbounded Operators on Hilbert Spaces.- 10 Spectral Theory III: Applications.- 11 Mathematical Formulation of Non-Relativistic Quantum Mechanics.- 12 Introduction to Quantum Symmetries.- 13 Selected Advanced Topics in Quantum Mechanics.- 14 Introduction to the Algebraic Formulation of Quantum Theories.- 15 Appendix A: Order Relations and Groups.- 16 Appendix B: Elements of Differential Geometry.