### Les fondements de la géométrie

Presses Universitaires de France, 1985

Summary based on review by H.W. Guggenheimer in Mathematical Reviews

This text on the foundations of geometry was developed for prospective teachers; it presupposes a good knowledge of the fundamentals of modern algebra with a solid abstract linear algebra course as a prerequisite. Topics include the construction of the fields of reals from formal decimal expansions, vector spaces including a brief study of the infinite-dimensional case with applications to Zorn's lemma, affine and projective geometry, translation planes and the relations between configuration theorems and algebraic properties, metric geometry, axiom systems including Euclid's axioms, and hyperbolic geometry. The book includes about 120 exercises of a theoretical nature. It is based on a course developed by the author at the Université Pierre-et-Marie-Curie (University of Paris 6) between 1979 and 1981.

**Contents**

- Le crops des réels
- Approfondissement de la structure vectorielle
- Approfondissement de la structure affine
- Eléments de géométrie projective
- Reconstruction axiomatique de la géométrie affine ou projective
- Géométrie métrique (euclidienne et non euclidienne)