Chapter 9 deals with the spectral analysis of extensions of a non-negative symmetric operator A in a separable Hilbert space \(\mathfrak H\) based on the boundary triple approach. In Sect. 9.1 limit behaviour of the Weyl function \(M(\cdot )\) of a non-negative symmetric operator A near 0 and \(-\infty \) is investigated and is used in the characterization of the Friedrichs and Kreı̆n extensions \(\widehat A_{\mathrm {F}}\) and \(\widehat A_{\mathrm {K}}\) in terms of the Weyl function. As a guiding tool, we present a result that relates the convergence of a sequence of quadratic forms bounded from below with the strong resolvent convergence of the corresponding operators. As is known the semiboundedness below property of a proper extension \(A_{B}\) of A, implies the semiboundedness below of the boundary operator B. In Sect. 9.2 the inverse implication, i.e., the SB property of A is discussed. Some criteria for the SB property of A are presented. In Sect. 9.3 we recall the theory of sectorial forms and their Friedrichs extensions and present a description of all sectorial proper extensions of a non-negative operator A. A series of examples including Sturm-Liouville operators, 2n-th order differential operators or Laplace operator in a domain with a piecewise smooth boundary, amply illustrate the material presented in this chapter.