In this chapter, we consider an optimal control problem with pointwise evaluation in the cost functional. Unlike the control problem discussed in Chap. 5 , which uses the \(L^2(\varOmega)\) norm in the cost functional, this setting relies on pointwise values of the state at a finite number of locations. This formulation is particularly relevant for practical applications involving pointwise measurements. In contrast to the problem with pointwise controls, see Chap. 10 , where the Dirac measures appear on the right-hand side of the state equation, here, they appear on the right-hand side of the adjoint equation. Moreover, while the results of Chap. 10 can be extended to arbitrary measures instead of the Dirac measures, cf. Remark 10.1.3 , in this chapter, we explicitly exploit the presence of Dirac measures in the adjoint equation, leading to the Green’s function type behavior of the corresponding solution. This allows us to show that although the adjoint state possesses in general only \(W^{1,p}(\varOmega)\) regularity with \(p<\frac {N}{N-1}\) , the optimal control is Lipschitz continuous. As the main result of this chapter, we provide error estimates for the finite element discretization of the considered problem.