The purpose of this book is to revive some of the beautiful results
obtained by various geometers of the 19th century, and to give its
readers a taste of concrete algebraic geometry. A good deal of space is
devoted to cross-ratios, conics, quadrics, and various interesting
curves and surfaces. The fundamentals of projective geometry are
efficiently dealt with by using a modest amount of linear algebra. An
axiomatic characterization of projective planes is also given. While the
topology of projective spaces over real and complex fields is described,
and while the geometry of the complex projective libe is applied to the
study of circles and Möbius transformations, the book is not restricted
to these fields. Interesting properties of projective spaces, conics,
and quadrics over finite fields are also given. This book is the first
volume in the Readings in Mathematics sub-series of the UTM. 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