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This book is unique in that it presents finite group theory through permutation matrices. Such a presentation leads to a much less cluttered and clearer presentation than is to be found in other books on group theory. The book is suitable for readers with no formal training in group theory and to individuals presently studying this subject. Group theory is playing an increasing role in modern physics, and knowledge of group theory is becoming essential to an understanding of physics. Hence, this book will also be of interest to physics students and to people with a general interest in physics. After presenting finite group theory, the book concludes with a skeleton outline of how the nature of our 4-dimensional space-time derives from the finite groups.