Good books and lecture notes to learn pseudo-differential operators and spectral theory I am looking for a list of good books and lecture notes to learn pseudo-differential operators and spectral theory (for infinite dimensions.)
I am familiar with introductory functional analysis, Sobolev spaces and Fourier Analysis. Books inclined towards partial differential equations is a plus. In particular, I intend to study fractional Laplacian operators.
Edit: Please note that it need not be a single book covering both the topics.
 A: Take a look at this graduate text text:
Spectral theory of linear differential operators and comparison algebras
By Heinz Otto Cordes, Cordes Heinz Otto · 1987
I think this book covers every topic you mentioned.
https://books.google.com/books?id=6WlLjznD2zwC&printsec=frontcover&dq=heinz+otto+cordes&hl=en&newbks=1&newbks_redir=1&sa=X&ved=2ahUKEwi8zJeg6cz2AhVbm2oFHaMcDRkQ6AF6BAgLEAI
A: For some references with specific material on both spectral theory and $\Psi$DO's, see

*

*Shubin's book "Pseudodifferential Operators and Spectral Theory" sounds perfect for you.

*Michael Taylor's 2nd PDE book contains two large chapters on both topics. He also has a more extensive textbook on pseudodifferential operators and nonlinear PDE.

*Dimassi and Sjostrand's "Spectral Asymptotics in the Semi-Classical Limit" covers both.

*Grigis and Sjostrand's "Microlocal Analysis for Differential Operators: An Introduction" covers both.

*Zworski's "Semiclassical Analysis" covers both and has many applications to PDE theory.

Also, see Textbook/monograph for microlocal analysis.
