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| Modern Elementary Geometry | |
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| The Beginnings of Geometry | |
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| Directed segments and angles | |
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| Ideal points and ratios | |
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| The theorem of Menelaus | |
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| Ceva's theorem | |
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| Some geometry of the triangle | |
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| More geometry of the triangle | |
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| Geometric constructions | |
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| Isometries in the Plane | |
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| The Amazing Greeks | |
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| Introduction to translations, rotations, and reflections | |
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| Introduction to isometries | |
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| Transformation theory | |
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| Isometries as products of reflections | |
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| Translations and rotations | |
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| Halfturns | |
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| Products of reflections | |
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| Properties of isometries; a summary | |
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| Applications of isometries to elementary geometry | |
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| Further elementary applications | |
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| Advanced applications | |
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| Analytic representations of direct isometries | |
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| Analytic representations of opposite isometries | |
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| Similarities in the Plane | |
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| The rebirth of mathematical thinking | |
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| Introduction to similarities | |
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| Homothety | |
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| Similarity | |
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| Applications of similarities to elementary geometry | |
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| Further elementary applications | |
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| Advanced applications | |
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| Analytic representations of similarities | |
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| Vectors and Complex Numbers in Geometry | |
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| The search for the meaning of complex numbers | |
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| Introduction to complex numbers | |
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| Vectors | |
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| Vector multiplication | |
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| Vectors and complex numbers | |
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| Triangles in the Gauss plane | |
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| Lines in the Gauss plane | |
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| The circle | |
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| Isometries and similarities in the Gauss plane | |
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| Inversion | |
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| Matchless modern mathematics | |
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| Inversion | |
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| Progressions, ratios, and Peaucellier's cell | |
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| Inversion and complex geometry | |
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| Applications of inversion | |
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| Isometries in Space | |
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| What next? | |
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| Introduction to three dimensions | |
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| Reflection in a plane | |
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| Basic space isometries | |
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| More space isometries | |
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| Some applications | |
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| Analytic representations | |
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| Appendixes | |
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| A Summary of Book I of Euclid's Elements | |
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| Basic Ruler and Compass Constructions | |
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| Bibliography | |
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| Hints for Selected Exercises | |
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| Answers | |
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| Index | |