These are notes from a graduate student course on algebraic topology and K-theory given by Daniel Quillen at the Massachusetts Institute of Technology during 1979-1980. He had just received the Fields Medal for his work on these topics among others and was funny and playful with a confident humility from the start. These are not meant to be polished lecture notes, rather, things are presented as did Quillen reflected in the hand-written notes, resisting any temptation to change or add notation, details or elaborations. Indeed, the text is faithful to Quillen's own exposition, even respecting the {\sl board-like presentation} of formulae, diagrams and proofs, omitting numbering theorems in favor of names and so on. This is meant to be Quillen on Quillen as it happened forty years ago, an informal text for a second-semester graduate student on topology, category theory and K-theory, a potential preface to studying Quillen's own landmark papers and an informal glimpse of his great mind. The intellectual pace of the lectures, namely fast and lively, is Quillen himself, and part of the point here is to capture some of this intimacy. To be sure, much has happened since then from this categorical perspective started by Grothendieck, and Misha Kapranov has contributed an Afterword in order to make it more useful to current students.

Autorentext

Robert Penner holds the Rene Thom Chair at the Institut des Hautes Etudes Scientifiques in Paris. His research extends across topology, geometry and combinatorics together with their applications to high energy physics and theoretical biology. Among his previous books are
Combinatorics of Train Tracks (Princeton University Press), Discrete Mathematics (World Scientific) and Decorated Teichmueller Theory
(European Mathematical Society).

Inhalt

Foreword.- Lecture 1.- Lecture 2.- Lecture 3.- Lecture 4.- Lecture 5.- Lecture 6.- Lecture 7.- Lecture 8.- Lecture 9.- Lecture 10.- Lecture 11.- Lecture 12.- Lecture 13.- Lecture 14.- Lecture 15.- Lecture 16.- Lecture 17.- Lecture 18.- Lecture 19.- Lecture 20.- Lecture 21.- Lecture 22.- Lecture 23.- Lecture 24.- Lecture 25.- Lecture 26.- Lecture 27.- Lecture 28.- Lecture 29.- Lecture 30.- Lecture 31.- Lecture 32.- Lecture 33.- Lecture 34.- Lecture 35.- Lecture 36.- Lecture 37.- Lecture 38.- Afterword by Mikhail Kapranov.- References.- Index.