Textbook in PDF format General spectral theory Closed operators The spectrum Spectral theory of compact operators Compact operators The Fredholm alternative Closed operators with compact resolvent Fredholm operators and the essential spectrum Appendix: The Dirichlet problem and boundary integrals Fourier transform, Sobolev spaces, and weak derivatives The Fourier transform Basic properties of Sobolev spaces Main results on Sobolev spaces Differential operators in Lp -spaces Appendix: Density, embedding and trace theorems Appendix: Tempered distributions Self-adjoint operators Basic properties The spectral theorems Holomorphic functional calculi The bounded case Sectorial operators Bibliography