The condition number of a matrix has a significant influence on the properties of the corresponding system of equations and the relationship between the norms of the residual vector and the error vector. In the previous chapter, we were already able to show for some Krylov subspace methods that a small condition number of the matrix ensures rapid convergence of the sequence of approximate solutions to the solution of the system. Motivated by this fact, it is natural to use an equivalent reformulation of the system with the aim of reducing the condition number of the matrix. Such techniques are referred to as preconditioning of the system and have proven to be an efficient means of accelerating and stabilizing Krylov subspace methods in the context of model problems as well as in other practical applications. In this chapter, we will therefore deal in detail with the description and investigation of possible preconditioning techniques.