This work on Abelian Group Theory (or Group Theory) to cover elementary results in Abelian Groups. It contains comprehensive coverage of almost all the topics related to the theory and is designed to be used as a course book for students at both undergraduate and graduate level. exercises in each chapter according to their level of difficulty starting with simples exercises (marked S1, S2 etc), medium difficulty (M1, M2 etc) and ending with the difficult exercises (D1, D2 etc). Solutions for all of the exercises are included. reference to a large number of examples in Group Theory.