Introductory book for homotopical algebra
I'm interested in learning homotopical algebra (by which I mean: model categories, simplicial methods, etc.) However, I've been unable to make heads or tails of any of the "standards" (Jardine&Goerss, Hovey, Hirschorn); they seem to presuppose knowledge of the subject material. What are some accessible introductions to this subject? (+ reading paths to get to the aforementioned "classics"?)
Background: I'm very comfortable with category theory and homological algebra, am learning enriched category theory, and have had a course in algebraic topology (and am currently studying more).
Solution 1:
Have you tried to read Hirschhorn, but starting on Part 2? -The first part is the real purpose of the book -localization of model category structures-, but more specialized and advanced. The second part is designed to serve as a support of that, more advanced, first part, and contains all the basics of homotopy theory (model categories). I would try, at least, with chapters 7, 8 and 9 -see what happens: I think it's not intended to be a "pedagogical" book on model categories, but a reference for the results on the first part. Nevertheless it is, first of all, systematic, and secondly, quite readable.
Solution 2:
I don't know if it is quite an introductory book but Quillen is not bad at all.
Dwyer and Spalinski is good as well.
There is a section in the Motivic homotopy theory book written by Bjorn Dundas (the section is by Dundas, the whole book is by a few other people as well). This might give the overall picture before you look for something more detailed.