John Bamberg is Associate Professor of Mathematics at the University of Western Australia, where he previously obtained his Ph.D. under the auspices of Cheryl Praeger and Tim Penttila. His research interests include finite and projective geometry, group theory, and algebraic combinatorics. He was a Marie Skłodowska-Curie fellow at Ghent University from 2006 to 2009, and a future fellow at the Australian Research Council from 2012 to 2016. Tim Penttila is an Australian mathematician whose research interests include geometry, group theory, and combinatorics. He was an academic at the University of Western Australia for twenty years, and a professor at Colorado State University for ten years.

'This book provides a lively and lovely perspective on real projective spaces, combining art, history, groups and elegant proofs.' William M. Kantor

• Preface; Part I. The Real Projective Plane: 1. Fundamental aspects of the real projective plane; 2. Collineations; 3. Polarities and conics; 4. Cross-ratio; 5. The group of the conic; 6. Involution; 7. Affine plane geometry viewed projectively; 8. Euclidean plane geometry viewed projectively; 9. Transformation geometry: Klein's point of view; 10. The power of projective thinking; 11. From perspective to projective; 12. Remarks on the history of projective geometry; Part II. Two Real Projective 3-Space: 13. Fundamental aspects of real projective space; 14. Triangles and tetrahedra; 15. Reguli and quadrics; 16. Line geometry; 17. Projections; 18. A glance at inversive geometry; Part III. Higher Dimensions: 19. Generalising to higher dimensions; 20. The Klein quadric and Veronese surface; Appendix: Group actions; References; Index.

John Bamberg is Associate Professor of Mathematics at the University of Western Australia, where he previously obtained his Ph.D. under the auspices of Cheryl Praeger and Tim Penttila. His research interests include finite and projective geometry, group theory, and algebraic combinatorics. He was a Marie Skłodowska-Curie fellow at Ghent University from 2006 to 2009, and a future fellow at the Australian Research Council from 2012 to 2016. Tim Penttila is an Australian mathematician whose research interests include geometry, group theory, and combinatorics. He was an academic at the University of Western Australia for twenty years, and a professor at Colorado State University for ten years.

'This book provides a lively and lovely perspective on real projective spaces, combining art, history, groups and elegant proofs.' William M. Kantor

• Preface; Part I. The Real Projective Plane: 1. Fundamental aspects of the real projective plane; 2. Collineations; 3. Polarities and conics; 4. Cross-ratio; 5. The group of the conic; 6. Involution; 7. Affine plane geometry viewed projectively; 8. Euclidean plane geometry viewed projectively; 9. Transformation geometry: Klein's point of view; 10. The power of projective thinking; 11. From perspective to projective; 12. Remarks on the history of projective geometry; Part II. Two Real Projective 3-Space: 13. Fundamental aspects of real projective space; 14. Triangles and tetrahedra; 15. Reguli and quadrics; 16. Line geometry; 17. Projections; 18. A glance at inversive geometry; Part III. Higher Dimensions: 19. Generalising to higher dimensions; 20. The Klein quadric and Veronese surface; Appendix: Group actions; References; Index.

John Bamberg is Associate Professor of Mathematics at the University of Western Australia, where he previously obtained his Ph.D. under the auspices of Cheryl Praeger and Tim Penttila. His research interests include finite and projective geometry, group theory, and algebraic combinatorics. He was a Marie Skłodowska-Curie fellow at Ghent University from 2006 to 2009, and a future fellow at the Australian Research Council from 2012 to 2016. Tim Penttila is an Australian mathematician whose research interests include geometry, group theory, and combinatorics. He was an academic at the University of Western Australia for twenty years, and a professor at Colorado State University for ten years.

'This book provides a lively and lovely perspective on real projective spaces, combining art, history, groups and elegant proofs.' William M. Kantor

• Preface; Part I. The Real Projective Plane: 1. Fundamental aspects of the real projective plane; 2. Collineations; 3. Polarities and conics; 4. Cross-ratio; 5. The group of the conic; 6. Involution; 7. Affine plane geometry viewed projectively; 8. Euclidean plane geometry viewed projectively; 9. Transformation geometry: Klein's point of view; 10. The power of projective thinking; 11. From perspective to projective; 12. Remarks on the history of projective geometry; Part II. Two Real Projective 3-Space: 13. Fundamental aspects of real projective space; 14. Triangles and tetrahedra; 15. Reguli and quadrics; 16. Line geometry; 17. Projections; 18. A glance at inversive geometry; Part III. Higher Dimensions: 19. Generalising to higher dimensions; 20. The Klein quadric and Veronese surface; Appendix: Group actions; References; Index.