Reinhold Baer and his influence on the theory of abelian groups

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Reinhold Baer's contributions to and influence on the theory of abelian groups are surveyed, concentrating on his publications on the theory of $p$-groups, torsion-free and mixed groups, subgroup lattices, endomorphism rings, the group Ext, as well as injective modules. His papers on these subjects were instrumental in the development of this branch of group theory.