Serre`s Problem on Projective Modules

This book covers the area of "Serre`s Problem on Projective Modules" thoroughly, and from very many different angles. It presents the broadest and most comprehensive view available in the literature on the mathematics of "Serre`s Conjecture". The author`s original treatment of Serre`s Conjecture in "Lecture Notes in Mathematics" (Vol. 635) has been completely worked over and expanded into a multifaceted exposition suitable for experts and yet easily accessible to beginners. Segments of new material in the book include an enriched coverage of stably free modules and the basic calculus of unimodular rows, Suslin`s Normality and n-Factorial Theorems, as well as his fundamental work on the K1 analogue of Serre`s Conjecture for polynomial rings. Another new feature of the book is a long survey chapter on the further developments in many acts and ramifications on Serre`s Problem that took place in the "post-Quillen-Suslin era", from 1977 to the present. TOC: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.