Projective Geometry

1. Projective Spaces.- 1.1 Projective Spaces and Projective Bases.- 1.2 Projective Transformations and the Projective Group.- 1.3 Projective and Affine Spaces.- 1.4 Axiomatic Presentation of Projective and Affine Planes.- 1.5 Projective Spaces of Hyperplanes and Duality.- 1.6 The Projective Space of Circles.- 1.7 The Projective Space of Conics.- 1.8 Projective Spaces of Divisors in Algebraic Geometry.- 2. One-Dimensional Projective Geometry.- 2.1 Cross-ratios and Rational Maps.- 2.2 Cross-ratios and permutations.- 2.3 Harmonic Division.- 2.4 Projective Transformations and Involutions on a Projective Line.- 2.5 The Projective Structure of a Conic.- 2.6 Unicursal Curves.- 2.7 The Complex Projective Line and the Circular Group.- 2.8 Topology of Projective Spaces.- 3. Classification of Conics and Quadrics.- 3.1 What Is a Quadric?.- 3.2 Classification of Affine and Euclidean Quadrics.- 3.3 Projective Classification of Real Quadrics.- 3.4 Classification of Conies and Quadrics over a Finite Field.- 4. Polarity with Respect to a Quadric.- 4.1 Polars and Poles.- 4.2 Polarity with Respect to Conics.- 4.3 Polarity and Tangential Equations.- 4.4 Applications to Conics.- Appendix: (2,2)-Correspondences.- Index of Symbols and Notations.

From the reviews: "...The book of P. Samuel thus fills a gap in the literature. It is a little jewel. Starting from a minimal background in algebra, he succeeds in 160 pages in giving a coherent exposition of all of projective geometry. ... one reads this book like a novel. " D.Lazard in Gazette des Mathématiciens#1