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This monograph gives a systematic exposition of this method for random lattice Schrödinger operators (LSO) with interaction. These results belong to the authors; many of them are presented for the first time in the literature. The authors focus on the Anderson tight binding model, which is most accessible to a broad audience. Also given is a detailed review of various relevant methods (generated, mainly, for the single-particle case), and a discussion of their strong and weak sides regarding their applicability to multi-particle systems.