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.
