Chapter 1 Introduction and Mathematical Backgrounds

Chapter 2 Normed and Banach Spaces, Examples and Applications

Chapter 3 Hilbert Spaces and Bounded Operators

Chapter 4 Families of Compact Operators on Hilbert Spaces and Fundamental Properties

Chapter 5 Densely-Defined Unbounded Operators on Hilbert Spaces

Chapter 6 Phenomenology of Quantum Systems and Wave Mechanics: An Overview

Chapter 7 The First 4 Axioms of QM: Propositions, Quantum States and Observables

Chapter 8 Spectral Theory I: Generalities, Abstract $$C^*$$ C ∗ -Algebras and Operators in $${\mathfrak B}({\mathsf H})$$ B ( H )

Chapter 9 Spectral Theory II: Unbounded Operators on Hilbert Spaces

Chapter 11 Mathematical Formulation of Non-relativistic Quantum Mechanics

Chapter 12 Introduction to Quantum Symmetries

Chapter 13 Selected Advanced Topics in Quantum Mechanics

Chapter 14 Introduction to the Algebraic Formulation of Quantum Theories