The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises. The main themes of the book are the following:- Spectral integrals and spectral decompositions of self-adjoint and normal operators- Perturbations of self-adjointness and of spectra of self-adjoint operators- Forms and operators- Self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extension | Unbounded Self-Adjoint Operators on Hilbert Space by Konrad Schmüdgen, Hardcover | Indigo Chapters