À la poursuite des champs (literally In Pursuit of Stacks, also Pursuing Stacks) is a soon-to-be-published manuscript written by Alexander Grothendieck in 1983. Its influence on higher category theory and homotopy theory is substantial. For an account of the origins, see Ronnie Brown’s account. Scanned copies of the original typescript are available here (in djvu, warning: 23MB) and here. Initially many of the copies of this important document were distributed from the School of Mathematics Bangor.
The manuscript starts with a letter to Daniel Quillen, and then proceeds as a sort of research diary, considering among other things, the notion of -groupoids and -groupoids, homotopy types and how to model them, homology and cohomology theories defined on categories of models and schematisation of homotopy types. This last is an attempt to define homotopy theory relative to a base ring, say, such that over ordinary homotopy theory is recovered. Due to the almost free-association style of authorship, there are many back-trackings, corrections and erroneous trains of thought. Despite this, the rich ideas lead to conjectures of considerable weight (bad sentence - I need a elf with an English major to help me :P), some of which have been proved by Denis-Charles Cisinski.
David Roberts: One thing which I’d like to see more in discussions about PS is that many of the ideas presented are now rigorously worked and published, and that it is not just some massive crazy work that merely has great influence.
The themes and ideas, especially those pertaining to the homotopy theory of diagrams, were further developed in Les Derivateurs.
To some extent the crux of the explicit link with stacks is described earlier in three letters from Grothendieck to Breen in 1975. (A commented version of these, other correspondence and the manuscipt (in LaTeX) is being prepared for publication shortly. Much of the material is being collected by the Grothendeick circle)