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The first aim of this book is to generalize this result from indecomposable modules to square-free ones by showing that an injective module is square-free if and only if its endomorphism ring is quasi-duo. The second aim is to describe all maximal right (left, two-sided) ideals of the endomorphism ring of an arbitrary injective module. And the third aim is to study two classes of modules: Loewy modules with finite Loewy invariants over an arbitrary ring and max modules with finite radical invariants over a semilocal ring.