In Chap. 3 some basic facts of extension theory of symmetric operators in Hilbert spaces are discussed. Section 3.2 presents a version of the Kato-Rellich theorem on strongly A-bounded perturbations of a symmetric (in particular, selfadjoint) operator A. In Sects. 3.3, 3.4 properties of isometric operators and Cayley transforms of symmetric operators are discussed. In Sect. 3.5 von Neumann construction of a selfadjoint extension of a symmetric operator A is modified for dissipative and accretive operators. Classical and generalized von Neumann formulas are presented in Sect. 3.6, their applications to the study of spectra of selfadjoint extensions of a symmetric operator are given in Sect. 3.8. A generalized Kreı̆n’s theorem ensuring that a symmetric operator with a gap admits a selfadjoint extension with an arbitrary prescribed point spectrum within the gap is also presented. In Section 3.10 the concepts of invariant and reducing subspaces of a linear operator are discussed and a theorem on the decomposition of a symmetric operator into a direct orthogonal sum of a simple and selfadjoint part is presented.