Visual Group Theory: A Computer-Oriented Geometric Introduction

“Symmetry is everywhere. Flowers, crystals, many natural phenomena and artifacts appear beautiful to us, especially in their symmetrical appearance. One may enjoy this beauty and leave it at that in admiration. Here, a systematic approach to symmetry is proposed. Mathematically, it should be made as widely and as generally understandable as possible.In the narrower sense, this book is about group theory. Groups can be considered as algebraic objects that describe the symmetry of geometric objects. This will mainly be the perspective adopted in the following, and thus, this book is also a book about geometry. Groups describe symmetry phenomena algebraically—one calculates with reflections, rotations, etc., generally with mappings of spaces onto themselves.”
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Visual Group Theory