In Chap. 2 we recall general concepts from the theory of unbounded linear operators in Hilbert spaces, such as closedness, closabilty and relative boundedness. In Sect. 2.4 some facts concerning T-bounded and strongly T-bounded perturbations are presented and in Sect. 2.5 an invariance result for the defect of a closed operator is proven. Spectral theorem for selfadjoint operators is discussed in Sect. 2.7. In Sect. 2.8 these notions are illustrated using the example of the differentiation operator. In Sect. 2.9 certain Hörmander results on estimates for minimal and maximal partial differential operators as well as their applications to the solvability of differential equations are discussed.