2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57461We survey recent results on spectral properties of random Schrödinger operators. The focus is set on the integrated density of states (IDS). First we present a proof of the existence of a self-averaging IDS which is general enough to be applicable to random Schrödinger and Laplace-Beltrami operators on manifolds. Subsequently we study more specific models in Euclidean space, namely of alloy type, and concentrate on the regularity properties of the IDS. We discuss the role of the integrated density of states and its regularity properties for the spectral analysis of random Schrödinger operators, particularly in relation to localisation. Proofs of the central results are given in detail. Whenever there are alternative proofs, the different approaches are compared.87 pages; corrected and extended versionMathematical PhysicsSpectral Theory35J10, 35P20, 81Q10, 81Q15; 58J35; 82B44text