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Synopsis This book presents the fundamental concepts and basic properties of groups, rings, factor groups and solvable groups, including the interplay between them and other mathematical branches and applied aspects. The aim of this book is not only to give the students quick access to the basic knowledge of algebra, either for future advancement in the field of algebra, or for general background information, but also to show that algebra is truly a master key or a "skeleton key" to many mathematical problems. As one knows, the teeth of an ordinary key prevent it from opening all but one door; whereas the skeleton key keeps only the essential parts, allow it to unlock many doors.

Some of the strengths of this undergraduate/graduate level textbook are the gentle introduction to proof in a concrete setting, the modern algebra concepts only after a careful study of important examples, and the gradual increase of the level of sophistication as the student progresses through the book. A number theory thread runs throughout several optional sections, and there is an overview of techniques for computing Galois groups. The book offers an extensive set of exercises that help to build skills in writing proofs. Chapter introductions, together with exercises at the ends of every chapters. Many examples and exercise are included to illustrate the power of intuitive approaches to algebra

The author wishes to present this book as an attempt to re-establish the contacts between algebra and other branches of mathematics and sciences.

Based on the author's years of teaching experience, this textbook provides students with a clear and carefully paced introduction to algebra. It begins with groups and rings, developing important concepts thoroughly before moving on to generating set. Later chapters then introduce a number of more advanced topics, including simple groups and extensions Matrix Rings, Jordan Holder's theorem and Syllow’s theorem.