Serre’s Conjecture 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 Serres 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