Inhaltsangabeto Serre's Conjecture: 1955-1976.- Foundations.- The "Classical" Results on Serre's Conjecture.- The Basic Calculus of Unimodular Rows.- Horrocks' Theorem.- Quillen's Methods.- K1-Analogue of Serre's Conjecture.- The Quadratic Analogue of Serre's Conjecture.- References for Chapters I-VII.- Appendix: Complete Intersections and Serre's Conjecture.- New Developments (since 1977).- References for Chapter VIII.

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Introduction.- The "Classical" Results on Serre''s Conjecture.- Two Elementary Proofs of Serre''s Conjecture.- Horrocks'' Theorem.- Quillen''s Method.- K1 Analogue of Serre''s Conjecture.- The Quadratic Analogue of Serre''s Conjecture.- New Developments (since 1977).- References.