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This book, in some sense, began to be written by the first author in 1983, when optional lectures on Abelian groups were held at the Fac- ulty of Mathematics and Computer Science, 'Babes-Bolyai' University in Cluj-Napoca, Romania. From 1992, these lectures were extended to a twosemester electivecourse on abelian groups for undergraduate stu- dents, followed by a twosemester course on the same topic for graduate students in Algebra. All the other authors attended these two years of lectures and are now Assistants to the Chair of Algebra of this Fac- ulty. The first draft of this collection,...