PDEs, functional analysis and operator theory

PDEs

Arnold, Lectures on partial differential equations

Evans, Partial differential equations

Taylor, Partial Differential Equations, vols. I-III

Han and Lin, Elliptic partial differential equations

Gilbarg and Trudinger, Elliptic partial differential equations of second order

Hormander, The analysis of linear partial differential operators, vols. I-IV

Pseudodifferential operators

Shubin, Pseudodifferential operators and spectral theory

Nagel and Stein, Lectures on pseudodifferential operators

Functional analysis and operator theory

Kolmogorov and Fomin, Elements of the theory of functions and functional analysis

Rudin, Functional analysis

Yosida, Functional analysis

Brezis, Functional analysis, Sobolev spaces and partial differential equations

Kreyszig, Introductory functional analysis with applications

Riesz and Nagy, Functional analysis

Halmos, Lectures on functional analysis and operator theory

Dunford and Schwartz, Linear operators, vols 1-3

Conway, A course in operator theory

Wiedmann, Linear operators on Hilbert spaces

Operator algebras

Murphy, C^*algebras and operator theory

Sakai, C*-algebras and W*-algebras

Stratila and Szido, Lectures on von Neumann algebras

Dixmier, Von Neumann algebras

Kadison and Ringrose, Fundamentals of the theory of operator algebras, vols 1-4

Semiclassical and microlocal analysis

Martines, An introduction to semiclassical and microlocal analysis

Guillemin and Sternberg, Semiclassical analysis

Zworski, Semiclassical analysis

Dimassi and Sjostrand, Spectral asymptotics in the semiclassical limit

Grigis and Sjostrand, Microlocal analysis for differential operators: an introduction

Various

Melrose, Geometric scattering theory

Reed and Simon, Methods of modern mathematical physics, vols 1-4