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, including only exercises
solved by students as home works, the last ten years, had 160pages. We
felt that there is a need for a book such as this one, because it would
provide a nice bridge between introductory Abelian Group Theory and more
advanced research problems. The book InfiniteAbelianGroups, published by
LaszloFuchsin two volumes 1970 and 1973 willwithout doubt last as the
most important guide for abelian group theorists. Many exercises are
selected from this source but there are plenty of other bibliographical
items (see the Bibliography) which were used in order to make up this
collection. For some of the problems stated, recent developments are
also given. Nevertheless, there are plenty of elementary results (the so
called 'folklore') in Abelian Group Theory whichdo not appear in any
written material. It is also one purpose of this book to complete this
gap.
