Derivators (in English)

For a few references in English, there are the papers of Heller, the main one being:

A. Heller, Homotopy theories, Mem. Amer. Math. Soc. 71 (383) (1988)

There is also a paper I wrote with A. Neeman, in which there is a little introduction to derivators in the second half of: Additivity for derivator K-theory, Adv. Math. 217 (2008), no. 4, 1381-1475

One can see derivators in action in the work of G. Tabuada (he explains Bousfield localization and stabilization in this setting, and compares with the model category point of view): Higher K-theory via universal invariants, Duke Math. J. 145 (2008), no. 1, 121–206 (availabe as arXiv:0706.2420).

George Maltsiniotis has given a mini-course in Seville last year, they include some handwritten notes in English, which are the part 3 of the course:

Lecture_III_Derivators.pdf

For the other parts of the course notes see the conference page.

Some very brief remarks on derivateurs are in Bertrand Toen's habilitation thesis on pages 12-14 and 27-29, available here. They mainly emphasize how derivateurs are sort of a 2-truncated homotopy theory of homotopy theories - nothing to learn derivateur-language from, but maybe a nice addition to the general picture.