I wish hereby to introduce the following two related books (covering similar subjects) to the interested:
1. Foundations of Quantum Theory: From Classical Concepts to Operator Algebras, by Klaas Landsman (University of Nijmegen, The Netherlands), Springer, xv-881pp, 2017
https://link.springer.com/book/10.1007%2F978-3-319-51777-3
This book is Open Access (free to download from the above page).
2. Spectral Theory and Quantum Mechanics: Mathematical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation, 2nd edition, by Valter Moretti (University of Trento, Italy), Springer, xxii-950pp, 2017
https://www.springer.com/gp/book/9783319707051
This text is a translation from an Italian original. Sadly, at places the translation is wanting (some sentences are convoluted, and at places tiresome, and I do hope that in preparing for the third edition of this most excellent book, Springer pays the necessary attention to correct for this major shortcoming).