Includes bibliographical references (pages 495-524) and index

Part I: Introduction and Motivation:
1. Subjects and User's Guide
Part II: Topics from Functional Analysis and Operators in Hilbert Space: A Selection
2. Elementary Facts
3. Unbounded Operators in Hilbert Space
4. Spectral Theory
Part III: Applications
5. GNS and Representations
6. Completely Positive Maps
7. Brownian Motion
8. Lie Groups, and Their Unitary Representations
9. The Kadison-Singer Problem
Part IV: Extension of Operators:
10. Selfadjoint Extensions
11. Unbounded Graph-Laplacians
12. Reproducing Kernel Hilbert Space

The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret "non-commutative analysis" broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)

A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.

The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.