From the Preface: "I felt it would be useful for graduate students to see a detailed account of the sequence of mathematical developments which was inspired by the Conjecture, and which ultimately led to its full solution.... I offered a course on Serre''s Conjecture to a small group of graduate students in January, 1977 [at the University of California, Berkeley] one year after its solution by Quillen and Suslin. My course was taught very much in the spirit of a mathematical ''guided tour''. Volunteering as the guide, I took upon myself the task of charting a route through all the beautiful mathematics surrounding the main problem to be treated; the ''guide'' then leads his audience through the route, on to the destination, pointing out the beautiful sceneries and historical landmarks along the way."

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Preface.- Introduction.- Foundations.- The "Classical" Results on Serre''s Conjecture.- Two Elementary Proofs of Serre''s Conjecture.- Horrocks'' Theorem.- Quillen''s Method.- The Quadratic Analogue of Serre''s Conjecture.- Appendix on Complete Intersections.- References.- Notations.- Index