This book is a systematic treatment of real algebraic geometry. It is carefully and clearly written; it starts with the basic concepts and leads to up-to-date research topics. The present volume is a translation, revision and updating of ERGEBNISSE vol.12, published in French in 1987. Many new developments in this field have been included in this book.

A systematic treatment of real algebraic geometry Carefully and clearly written may serve as a basis for a graduate course Many of the new developments are included in this edition

Inhalt

1. Ordered Fields, Real Closed Fields.- 2. Semi-algebraic Sets.- 3. Real Algebraic Varieties.- 4. Real Algebra.- 5. The Tarski-Seidenberg Principle as a Transfer Tool.- 6. Hilbert's 17th Problem. Quadratic Forms.- 7. Real Spectrum.- 8. Nash Functions.- 9. Stratifications.- 10. Real Places.- 11. Topology of Real Algebraic Varieties.- 12. Algebraic Vector Bundles.- 13. Polynomial or Regular Mappings with Values in Spheres.- 14. Algebraic Models of C? Manifolds.- 15. Witt Rings in Real Algebraic Geometry.- Index of Notation.