Chapter 11 deals with operators associated with the three-coefficient differential Sturm–Liouville expression \({\mathcal A}\) . We present some known facts concerning the differential operators generated by \({\mathcal A}\) using the boundary triple approach. In Sect. 11.2 some known facts on a regular Sturm-Liouville operator on a finite interval are presented. In this case the resolvents of boundary value problems are computed by using the Kreı̆n resolvent formula. The Weyl function technique is applied to investigate selfadjoint realizations with separated boundary conditions, their interlacing properties are proved. To characterize the spectra of selfadjoint realizations with \(\theta \) -periodic (including periodic and antiperiodic) boundary conditions we find a relation between the Weyl function and the Lyapunov function (Hill discriminant). Applying Weyl function we also establish classical inequalities between eigenvalues of periodic, antiperiodic, and Dirichlet (Neumann) realizations. In Sect. 11.3 we investigate boundary value problems for Sturm-Liouville operator with one or two singular endpoints. In particular, we discuss here periodic Sturm-Liouville operator on the line (half-line) and establish absolute continuity and the band-zone structure of its spectrum. To this end we apply the coupling construction from Chap. 8. In Sect. 11.4 we discuss the Sturm-Liouville operator semibounded below in \(L^2(\Bbb R_+)\) with both a semibounded potential and a non-semibounded oscillating potential. We also consider Moser’s example of a non-negative Sturm-Liouville operator in \(L^2(\Bbb R_+)\) for which domain of the minimal operator is not imbedded in \(H^1(\Bbb R_+)\) . In Sect. 11.5 we exhibit the domains of minimal and maximal singular Bessel operators in \(L^2(\Bbb R_+)\) , define an appropriate boundary triple and compute the corresponding Weyl function. The Friedrichs’ and Kreı̆n extensions are also described via boundary conditions.